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An updated review of goodness-of-fit tests for regression models. (English) Zbl 1273.62086
Summary: This survey intends to collect the developments on goodness-of-fit for regression models during the last 20 years, from the very first origins with the proposals based on the idea of the tests for density and distribution, until the most recent advances for complex data and models. Far from being exhaustive, the contents in this paper are focused on two main classes of tests statistics: smoothing-based tests (kernel-based) and tests based on empirical regression processes, although other tests based on maximum likelihood ideas will be also considered. Starting from the simplest case of testing a parametric family for regression curves, the contributions in this field provide also testing procedures in semiparametric, nonparametric, and functional models, dealing also with more complex settings, as those ones involving dependent or incomplete data.

MSC:
62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
62-02 Research exposition (monographs, survey articles) pertaining to statistics
Software:
fda (R)
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[1] Ahmad IA, Cerrito PB (1993) Goodness-of-fit tests based on the L 2-norm of multivariate probability density functions. J Nonparametr Stat 2:169–181 · Zbl 1360.62206 · doi:10.1080/10485259308832550
[2] Aït-Sahalia Y (1996) Testing continuous time models of the spot interest rate. Rev Financ Stud 9:385–426 · doi:10.1093/rfs/9.2.385
[3] Aït-Sahalia Y, Fan J, Jiang J (2010) Nonparametric test of the Markov hypothesis in continuous–time models. Ann Stat 38:3129–3163 · Zbl 1200.62044 · doi:10.1214/09-AOS763
[4] Akritas M, Van Keilegom I (2001) Nonparametric estimation of the residual distribution. Scand J Stat 28:549–567 · Zbl 0980.62027 · doi:10.1111/1467-9469.00254
[5] Albers CJ, Schaafsma W (2008) Goodness of fit testing using a specific density estimate. Stat Decis 26:3–23 · Zbl 1418.62188
[6] Alcalá T, Cristóbal JA, González-Manteiga W (1999) Goodness of fit test for linear models based on local polynomials. Stat Probab Lett 42:39–46 · Zbl 0946.62016 · doi:10.1016/S0167-7152(98)00184-9
[7] Aneiros-Pérez G, González-Manteiga W, Vieu P (2004) Estimation and testing in a partial linear regression model under long-memory dependence. Bernoulli 10:49–78 · Zbl 1040.62028 · doi:10.3150/bj/1077544603
[8] Arapis M, Gao J (2006) Empirical comparisons in short–term interest rate models using nonparametric methods. J Financ Econom 4:310–345 · doi:10.1093/jjfinec/nbj007
[9] Azzalini A, Bowman AW (1993) On the use of nonparametric regression for checking linear relationships. J R Stat Soc B 55:549–557 · Zbl 0800.62222
[10] Azzalini A, Bowman AW, Härdle W (1989) On the use of nonparametric regression models. Biometrika 76:1–11 · Zbl 0663.62096 · doi:10.1093/biomet/76.1.1
[11] Bachmann D, Dette H (2005) A note on the Bickel-Rosenblatt test in autoregressive time series. Stat Probab Lett 74:221–234 · Zbl 1070.62067 · doi:10.1016/j.spl.2005.04.003
[12] Beran R (1981) Nonparametric regression with randomly censored survival data. Technical report, University of California, Berkeley
[13] Berkson J (1950) Are these two regressions? J Am Stat Assoc 45:164–180 · Zbl 0040.22404 · doi:10.1080/01621459.1950.10483349
[14] Bickel PJ, Rosenblatt M (1973) On some global measures of the deviations of density function estimates. Ann Stat 1:1071–1095 · Zbl 0275.62033 · doi:10.1214/aos/1176342558
[15] Biederman S, Dette H (2000) Testing linearity of regression models with dependent errors by kernel-based methods. Test 9:417–438 · Zbl 1107.62324 · doi:10.1007/BF02595743
[16] Biederman S, Dette H (2001) Optimal designs for testing the functional form of a regression via nonparametric estimation techniques. Stat Probab Lett 52:215–224 · Zbl 1012.62079 · doi:10.1016/S0167-7152(00)00244-3
[17] Bierens HJ (1982) Consistent model especification tests. J Econom 20:105–134 · Zbl 0549.62076 · doi:10.1016/0304-4076(82)90105-1
[18] Brockwell PJ, Davis RA (1991) Time series: theory and methods, 2nd edn. Springer, Berlin
[19] Bücher A, Dette H (2010) Some comments on goodness-of-fit tests for the parametric form of the copula based on L 2-distances. J Multivar Anal 101:749–763 · Zbl 1181.62060 · doi:10.1016/j.jmva.2009.09.014
[20] Bücher A, Dette H, Wieczorek G (2011) Testing model assumptions in functional regression models. J Multivar Anal 102:1472–1488 · Zbl 1219.62075 · doi:10.1016/j.jmva.2011.05.014
[21] Cao R, González-Manteiga W (1993) Bootstrap methods in regression smoothing. J Nonparametr Stat 2:379–388 · Zbl 1360.62202 · doi:10.1080/10485259308832566
[22] Cao R, González-Manteiga W (2008) Goodness-of-fit tests for conditional models under censoring and truncation. J Econom 143:166–190 · Zbl 1418.62190 · doi:10.1016/j.jeconom.2007.08.011
[23] Cao R, Lugosi G (2005) Goodness-of-fit tests based on the kernel density estimate. Scand J Stat 32:599–616 · Zbl 1091.62031 · doi:10.1111/j.1467-9469.2005.00471.x
[24] Carroll RJ, Ruppert D (1988) Transformation and weighting in regression. Chapman and Hall, New York · Zbl 0666.62062
[25] Carroll RJ, Delaigle A, Hall P (2011) Testing and estimating shape-constrained nonparametric density and regression in the presence of measurement error. J Am Stat Assoc 106:191–202 · Zbl 1396.62084 · doi:10.1198/jasa.2011.tm10355
[26] Chabot-Hallé D, Duchesne P (2008) Diagnostic checking of multivariate nonlinear time series models with martingale difference errors. Stat Probab Lett 78:997–1005 · Zbl 1141.62064 · doi:10.1016/j.spl.2007.10.003
[27] Chebana F (2004) On the optimization of the weighted Bickel–Rosenblatt test. Stat Probab Lett 68:333–345 · Zbl 1086.62044 · doi:10.1016/j.spl.2004.03.007
[28] Chebana F (2006) Functional asymptotic normality of the L 2-deviation of the kernel density estimation indexed by classes of weight functions. J Stat Plan Inference 136:2470–2505 · Zbl 1091.60001 · doi:10.1016/j.jspi.2004.11.004
[29] Chen SX, Cui H (2003) An extended empirical likelihood for generalized linear models. Stat Sin 13:69–81 · Zbl 1017.62061
[30] Chen SX, Gao J (2007) An adaptive empirical likelihood test for parametric time series regression models. J Econom 141:950–972 · Zbl 1418.62191 · doi:10.1016/j.jeconom.2006.12.002
[31] Chen SX, Van Keilegom I (2009a) A goodness of fit test for parametric and semiparametric models in multiresponse regression. Bernoulli 15:955–976 · Zbl 1200.62047 · doi:10.3150/09-BEJ208
[32] Chen SX, Van Keilegom I (2009b) A review on empirical likelihood methods for regression. Test 18:415–447 · Zbl 1203.62035 · doi:10.1007/s11749-009-0159-5
[33] Chen SX, Härdle W, Li M (2003) An empirical likelihood goodness of fit test for time series. J R Stat Soc B 65:663–678 · Zbl 1063.62064 · doi:10.1111/1467-9868.00408
[34] Chen SX, Gao J, Tang CY (2008) A test for model specification of difussion processes. Ann Stat 36:167–198 · Zbl 1132.62063 · doi:10.1214/009053607000000659
[35] Chiou JM, Muller HG (2007) Diagnostics for functional regression via residual processes. Comput Stat Data Anal 51:4849–4863 · Zbl 1162.62394 · doi:10.1016/j.csda.2006.07.042
[36] Corradi V, Swanson N (2005) Bootstrap specification tests for diffusion processes. J Econom 124:117–148 · Zbl 1337.62193 · doi:10.1016/j.jeconom.2004.02.013
[37] Corradi V, White H (1999) Specification tests for the variance of a difussion. J Time Ser Anal 20:253–270 · Zbl 0932.62095 · doi:10.1111/1467-9892.00136
[38] Cox DR (1969) Some sampling problems in technology. In: New developments in survey sampling. Springer, Berlin, pp 506–527
[39] Cox DR (1972) Regression models and life tables. J R Stat Soc B 34:187–200 · Zbl 0243.62041
[40] Cressie N (1993) Statistics for spatial data. Wiley, New York
[41] Crujeiras RM, Fernández-Casal R, González-Manteiga W (2007) Comparing spatial dependence structures using spectral density estimators. Environmetrics 18:793–808 · doi:10.1002/env.879
[42] Crujeiras RM, Fernández-Casal R, González-Manteiga W (2008) An l2-test for comparing spatial spectral densities. Stat Probab Lett 78:2543–2551 · Zbl 1146.62070 · doi:10.1016/j.spl.2008.02.027
[43] Crujeiras RM, Fernández-Casal R, González-Manteiga W (2010a) Goodness-of-fit tests for the spatial spectral density. Stoch Environ Res Risk Assess 24:67–78 · doi:10.1007/s00477-008-0300-0
[44] Crujeiras RM, Fernández-Casal R, González-Manteiga W (2010b) Nonparametric test for separability of spatio–temporal processes. Environmetrics 21:382–399 · doi:10.1002/env.1006
[45] Cuesta-Albertos JA, del Barrio E, Fraiman R, Matrán C (2007) The random projection method in goodness of fit for functional data. Comput Stat Data Anal 51:4814–4831 · Zbl 1162.62363 · doi:10.1016/j.csda.2006.09.007
[46] de Jong P (1987) A central limit theorem for generalized quadratic forms. Probab Theory Relat Fields 75:261–277 · Zbl 0596.60022 · doi:10.1007/BF00354037
[47] Debbarh M, Viallon V (2008) Testing additivity in nonparametric regression under random censorship. Stat Probab Lett 78:2584–2591 · Zbl 1147.62328 · doi:10.1016/j.spl.2008.07.027
[48] Delgado M (1993) Testing the equality of nonparametric regression curves. Stat Probab Lett 17:199–204 · Zbl 0771.62034 · doi:10.1016/0167-7152(93)90167-H
[49] Delgado M, González-Manteiga W (2001) Significance testing in nonparametric regression based on the bootstrap. Ann Stat 29:1469–1507 · Zbl 1043.62032 · doi:10.1214/aos/1013203462
[50] Delgado M, Velasco C (2010) Distribution–free tests for time series models specification. J Econom 108:25–42 · Zbl 1431.62363
[51] Delgado M, Hidalgo J, Velasco C (2005) Distribution free goodness-of-fit tests for linear processes. Ann Stat 33:2568–2609 · Zbl 1084.62038 · doi:10.1214/009053605000000606
[52] Delsol L, Ferraty F, Vieu P (2011a) Structural test in regression on functional variables. J Multivar Anal 102:422–447 · Zbl 1207.62096 · doi:10.1016/j.jmva.2010.10.003
[53] Delsol L, Ferraty F, Vieu P (2011b) Focusing on structural assumptions in regression on functional variable. In: Recent advances in functional data analysis and related topics. Springer, Berlin, pp 77–82
[54] Derbort S, Dette H, Munk A (2002) A test for additivity in nonparametric regression. Ann Inst Stat Math 54:60–82 · Zbl 0991.62023 · doi:10.1023/A:1016113704805
[55] Dette H (1999) A consistent test for the functional form of a regression based on a difference of variance estimators. Ann Stat 27:1012–1040 · Zbl 0957.62036 · doi:10.1214/aos/1018031266
[56] Dette H (2002) A consistent test for heteroscedasticity in nonparametric regression based on the kernel method. J Stat Plan Inference 103:311–329 · Zbl 0988.62024 · doi:10.1016/S0378-3758(01)00229-4
[57] Dette H, Heuchenne C (2012) Scale checks in censored regression. Scand J Stat 39:323–339 · Zbl 1246.62102 · doi:10.1111/j.1467-9469.2011.00788.x
[58] Dette H, Hildebrandt T (2012) A note on testing hypotheses for stationary processes in the frequency domain. J Multivar Anal 104:101–114 · Zbl 1236.62101 · doi:10.1016/j.jmva.2011.07.002
[59] Dette H, Marchlewski M (2008) A test for the parametric form of the variance function in a partial linear regression model. J Stat Plan Inference 138:3005–3021 · Zbl 1140.62029 · doi:10.1016/j.jspi.2007.11.007
[60] Dette H, Munk A (1998) Testing heterocedasticity in nonparametric regression. J R Stat Soc B 60:693–708 · Zbl 0909.62035 · doi:10.1111/1467-9868.00149
[61] Dette H, Neumeyer N (2001) Nonparametric analysis of covariance. Ann Stat 29:1361–1400 · Zbl 1043.62033 · doi:10.1214/aos/1013203458
[62] Dette H, Paparoditis W (2009) Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities. J R Stat Soc B 71:831–857 · Zbl 1248.62145 · doi:10.1111/j.1467-9868.2009.00709.x
[63] Dette H, Podolskij M (2008) Testing the parametric form of the volatility in continuous time diffusion models–a stochastic process approach. J Econom 143:56–73 · Zbl 1418.62284 · doi:10.1016/j.jeconom.2007.08.002
[64] Dette H, von Lieres und Wilkau C (2001) Testing additivity by kernel methods–what is a reasonable test? Bernoulli 7:669–697 · Zbl 1005.62037 · doi:10.2307/3318732
[65] Dette H, von Lieres und Wilkau C (2003) On a test for a parametric form of volatility in continuous time financial models. Finance Stoch 7:363–384 · Zbl 1067.62087 · doi:10.1007/s007800200087
[66] Dette H, Weissbach R (2009) A bootstrap test for the comparison of nonlinear time series. Comput Stat Data Anal 53:1339–1349 · Zbl 1452.62627 · doi:10.1016/j.csda.2008.11.014
[67] Dette H, von Lieres und Wilkau C, Sperlich S (2005) A comparison of different nonparametric methods for inference on additive models. J Nonparametr Stat 17:57–81 · Zbl 1055.62039 · doi:10.1080/10485250410001713972
[68] Dette H, Podolskij M, Vetter M (2006) Estimation of interpreted volatility in continuous–time financial models with applications to goodness-of-fit. Scand J Stat 33:259–278 · Zbl 1125.62084 · doi:10.1111/j.1467-9469.2006.00479.x
[69] Dette H, Neumeyer N, Van Keilegom I (2007) A new test for the parametric form of the variance function in nonparametric regression. J R Stat Soc B 69:903–971 · doi:10.1111/j.1467-9868.2007.00616.x
[70] Dette H, Wagener J, Volgushev S (2011) Comparing conditional quantile curves. Scand J Stat 38:63–88 · Zbl 1246.62119 · doi:10.1111/j.1467-9469.2010.00718.x
[71] Diblasi AM, Bowman AW (1997) Testing for constant variance in a linear model. Stat Probab Lett 33:95–103 · Zbl 0901.62064 · doi:10.1016/S0167-7152(96)00115-0
[72] Diblasi AM, Bowman AW (2001) On the use of the variogram in checking for independence in spatial data. Biometrics 57:211–218 · Zbl 1209.62209 · doi:10.1111/j.0006-341X.2001.00211.x
[73] Diblasi AM, Maglione D (2004) Exploring a valid model for the variogram of an isotropic spatial process. Stoch Environ Res Risk Assess 18:366–376 · Zbl 1056.62106 · doi:10.1007/s00477-003-0143-7
[74] Diebolt J (1995) A nonparametric test for the regression function: asymptotic theory. J Stat Plan Inference 44:1–17 · Zbl 0812.62051 · doi:10.1016/0378-3758(94)00045-W
[75] Diebolt J, Zuber J (1999) Goodness-of-fit tests for nonlinear heteroscedastic regression models. Stat Probab Lett 42:53–60 · Zbl 0947.62032 · doi:10.1016/S0167-7152(98)00189-8
[76] Diebolt J, Zuber J (2001) On testing goodness-of-fit of nonlinear heteroscedastic regression models. Commun Stat, Simul Comput 30:195–216 · Zbl 1008.62533 · doi:10.1081/SAC-100001867
[77] Dominguez MA, Lobato IN (2003) Testing the martingale difference hypothesis. Econom Rev 22:351–377 · Zbl 1030.62066 · doi:10.1081/ETC-120025895
[78] Durbin J (1973) Weak convergence of the sample distribution function when parameters are estimated. Ann Stat 1:279–290 · Zbl 0256.62021 · doi:10.1214/aos/1176342365
[79] Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1–26 · Zbl 0406.62024 · doi:10.1214/aos/1176344552
[80] Eichler M (2008) Testing nonparametric and semiparametric hypothesis in vector stationary processes. J Multivar Anal 99:968–1009 · Zbl 1136.62371 · doi:10.1016/j.jmva.2007.06.003
[81] Escanciano JC (2004) Contrastes de especificación en modelos econométricos de series temporales. PhD thesis, University Carlos III
[82] Escanciano JC (2006a) Goodness of fit tests for linear and nonlinear time series models. J Am Stat Assoc 101:531–541 · Zbl 1119.62359 · doi:10.1198/016214505000001050
[83] Escanciano JC (2006b) A consistent diagnostic test for regression models using projections. Econom Theory 22:1030–1051 · Zbl 1170.62318
[84] Escanciano JC (2007a) Model checks using residual marked empirical processes. Stat Sin 17:115–138 · Zbl 1145.62071
[85] Escanciano JC (2007b) Weak convergence of non-stationarity multivariate marked processes with applications to martingale testing. J Multivar Anal 98:1321–1336 · Zbl 1116.62084 · doi:10.1016/j.jmva.2007.03.004
[86] Escanciano JC (2009) On the lack of power of omnibus specification tests. Econom Theory 25:162–194 · Zbl 1231.62079 · doi:10.1017/S0266466608090051
[87] Escanciano JC, Song K (2009) Testing single–index restrictions with a focus on average derivatives. J Econom 156:377–391 · Zbl 1431.62610 · doi:10.1016/j.jeconom.2009.11.007
[88] Escanciano JC, Velasco C (2006a) Generalized spectral tests for the martingale difference hypothesis. J Econom 134:151–185 · Zbl 1418.62320 · doi:10.1016/j.jeconom.2005.06.019
[89] Escanciano JC, Velasco C (2006b) Testing the martingale difference using integrated regression functions. Comput Stat Data Anal 51:2278–2294 · Zbl 1157.62488 · doi:10.1016/j.csda.2006.07.039
[90] Escanciano JC, Velasco C (2010) Specification tests of parametric dynamic conditional quantiles. J Econom 159:209–221 · Zbl 1431.62186 · doi:10.1016/j.jeconom.2010.06.003
[91] Eubank RL, Hart J (1992) Testing goodness-of-fit in regression via ordered selection criteria. Ann Stat 20:1412–1425 · Zbl 0776.62045 · doi:10.1214/aos/1176348775
[92] Eubank RL, Hart J (1993) Commonality of Cusum, von Neumann and smoothing-based goodness-of-fit tests. Biometrika 80:89–98 · Zbl 0792.62042 · doi:10.1093/biomet/80.1.89
[93] Eubank RL, LaRiccia V (1993) Testing for no effect in nonparametric regression. J Stat Plan Inference 36:1–14 · Zbl 0771.62035 · doi:10.1016/0378-3758(93)90097-P
[94] Eubank RL, Hart J, Simpson DP, Stefanski L (1995) Testing for additivity in nonparametric regression. Ann Stat 23:1896–1920 · Zbl 0858.62036 · doi:10.1214/aos/1034713639
[95] Eubank RL, Ching-Shang L, Wang S (2005) Testing lack of fit of parametric regression models using nonparametric regression techniques. Stat Sin 15:135–152 · Zbl 1059.62042
[96] Fan J, Gijbels I (1996) Local polynomial modelling and its applications, Monographs on statistics and applied probability. Chapman & Hall, London · Zbl 0873.62037
[97] Fan J, Jiang J (2005) Nonparametric inference for additive models. J Am Stat Assoc 100:890–907 · Zbl 1117.62328 · doi:10.1198/016214504000001439
[98] Fan J, Jiang J (2007) Nonparametric inference with generalized likelihood ratio tests. Test 16:409–444 · Zbl 1131.62035 · doi:10.1007/s11749-007-0080-8
[99] Fan J, Zhang C (2003) A reexamination of diffusion estimators with applications to financial model validation. J Am Stat Assoc 98:118–134 · Zbl 1073.62571 · doi:10.1198/016214503388619157
[100] Fan J, Zhang W (2004) Generalized likelihood ratio tests for spectral density. Biometrika 89:195–209 · Zbl 1132.62351 · doi:10.1093/biomet/91.1.195
[101] Fan J, Zhang C, Zhang J (2001) Generalised likelihood ratio statistics and Wilks phenomenon. Ann Stat 29:153–193 · Zbl 1029.62042 · doi:10.1214/aos/996986505
[102] Fan J, Jiang J, Zhang C, Zhou Z (2003) Time–dependent diffusion models for term structure dynamics. Stat Sin 13:965–992 · Zbl 1065.62177
[103] Fan Y (1994) Testing the goodness of fit of a parametric density function by the kernel method. Econom Theory 10:316–356 · Zbl 04520945 · doi:10.1017/S0266466600008434
[104] Fan Y (1998) Goodness-of-fit tests based on kernel density estimators with fixed smoothing parameters. Econom Theory 14:604–621
[105] Fan Y, Li Q (1996) Consistent model specification tests: omitted variables and semiparametric functional forms. Econometrica 64:865–890 · Zbl 0854.62038 · doi:10.2307/2171848
[106] Fan Y, Linton O (2003) Some higher–order theory for a consistent non-parametric model specification test. J Stat Plan Inference 109:125–154 · Zbl 1008.62042 · doi:10.1016/S0378-3758(02)00307-5
[107] Fermanian JD (2005) Goodness-of-fit tests for copulas. J Multivar Anal 95:119–152 · Zbl 1095.62052 · doi:10.1016/j.jmva.2004.07.004
[108] Ferraty F, Romain Y (2010) The Oxford handbook on functional data analysis. Oxford University Press, Oxford
[109] Ferraty F, Vieu P (2006) Nonparametric functional data analysis. Springer, New York · Zbl 1119.62046
[110] Ferreira E, Stute W (2004) Testing for differences between conditional means in a time series context. J Am Stat Assoc 99:169–174 · Zbl 1089.62516 · doi:10.1198/016214504000000160
[111] Franke J, Kreiss JP, Mammen E (2002) Bootstrap of kernel smoothing in nonlinear time series. Bernoulli 8:1–38 · Zbl 1006.62038
[112] Gao J (2007) Nonlinear time series. Semiparametric and nonparametric methods. Chapman and Hall, London · Zbl 1179.62118
[113] Gao J, Casas I (2008) Specification testing in continuous–time diffusion models. Theory and practice. J Econom 147:131–140 · Zbl 1429.62468 · doi:10.1016/j.jeconom.2008.09.006
[114] Gao J, Gijbels I (2008) Bandwidth selection in nonparametric kernel testing. J Am Stat Assoc 103:1584–1594 · Zbl 1286.62043 · doi:10.1198/016214508000000968
[115] Gao J, King M (2004) Adaptative testing in continuous–time diffussion models. Econom Theory 20:844–882 · Zbl 1071.62068
[116] Gao J, King Z, Lu M, Tjøstheim D (2009) Specification testing in nonlinear and nonstationary time series autoregression. Ann Stat 37:3893–3928 · Zbl 1191.62148 · doi:10.1214/09-AOS698
[117] Gasser T, Müller HG (1979) Kernel estimation of regression functions. In: Smoothing techniques for curve estimation. Lecture notes in mathematics, vol 757. Springer, Berlin
[118] Gijbels I, Rousson V (2001) A nonparametric least-squares test for checking a polynomial relationship. Stat Probab Lett 51:253–261 · Zbl 0965.62038 · doi:10.1016/S0167-7152(00)00152-8
[119] Giné E, Mason DM (2004) The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator. Bernoulli 4:721–752 · Zbl 1067.62048 · doi:10.3150/bj/1093265638
[120] González-Manteiga W, Aneiros-Pérez G (2003) Testing in partial linear regression models with dependent errors. J Nonparametr Stat 15:93–111 · Zbl 1019.62056 · doi:10.1080/10485250306033
[121] González-Manteiga W, Cadarso-Suárez C (1994) Asymptotic properties of a generalized Kaplan–Meier estimator with some applications. J Nonparametr Stat 4:65–78 · Zbl 1383.62142 · doi:10.1080/10485259408832601
[122] González-Manteiga W, Cao R (1993) Testing the hypothesis of a general linear model using nonparametric regression estimation. Test 2:161–188 · Zbl 0811.62044 · doi:10.1007/BF02562674
[123] González-Manteiga W, Pérez-González A (2006) Goodness-of-fit tests for linear regression models with missing response data. Can J Stat 34:149–170 · Zbl 1096.62041 · doi:10.1002/cjs.5550340111
[124] González-Manteiga W, Vilar-Fernández J (1995) Testing linear regression models using non-parametric regression estimators when errors are non-independent. Comput Stat Data Anal 20:521–541 · Zbl 0900.62192 · doi:10.1016/0167-9473(94)00058-Q
[125] González-Manteiga W, Quintela-del Río A, Vieu P (2002) A note on variable selection in nonparametric regression with dependent data. Stat Probab Lett 57:259–268 · Zbl 0996.62036 · doi:10.1016/S0167-7152(02)00056-1
[126] González-Manteiga W, Heuchenne C, Sánchez-Sellero C (2007) Parametric conditional mean and variance testing with censored data. In: Recent advances in applied stochastic models and data analysis. World Scientific, Singapore
[127] Gouriéroux C, Tenreiro C (2001) Local power properties of kernel based goodness of fit tests. J Multivar Anal 78:161–190 · Zbl 1081.62529 · doi:10.1006/jmva.2000.1950
[128] Gozalo PL, Linton O (2001) Testing additivity in generalized nonparametric regression models with estimated parameters. J Econom 104:1–48 · Zbl 0978.62032 · doi:10.1016/S0304-4076(01)00049-5
[129] Grigoletto M, Akritas MG (1999) Analysis of covariance with incomplete data via semiparametric model transformations. Biometrics 55:1177–1187 · Zbl 1059.62657 · doi:10.1111/j.0006-341X.1999.01177.x
[130] Gu J, Li D, Liu D (2007) Bootstrap nonparametric significance test. J Nonparametr Stat 19:215–230 · Zbl 1130.62032 · doi:10.1080/10485250701734497
[131] Guerre E, Lavergne P (2002) Optimal minimax rates for nonparametric specification testing in regression models. Econom Theory 18:1139–1171 · Zbl 1033.62042
[132] Guerre E, Lavergne P (2005) Data-driven rate optimal specification testing in regression models. Ann Stat 33:840–870 · Zbl 1068.62055 · doi:10.1214/009053604000001200
[133] Guyon X (1982) Parameter estimation for a stationary process on a d-dimensional lattice. Biometrika 69:95–105 · Zbl 0485.62107
[134] Hall P, Hart JD (1990) Bootstrap test for difference between means in nonparametric regression. J Am Stat Assoc 85:1039–1049 · Zbl 0717.62037 · doi:10.1080/01621459.1990.10474974
[135] Hall P, Ma Y (2007) Testing the suitability of polynomial models in error-in-variables problems. Ann Stat 35:2620–2638 · Zbl 1129.62042 · doi:10.1214/009053607000000361
[136] Hall P, Yatchew A (2005) Unified approach to testing functional hypotheses in semiparametric contexts. J Econom 127:225–252 · Zbl 1334.62080 · doi:10.1016/j.jeconom.2004.08.005
[137] Hall P, Huber C, Speckman PL (1997) Covariate-matched one-sided tests for the difference between functional means. J Am Stat Assoc 92:1074–1083 · Zbl 0889.62033 · doi:10.1080/01621459.1997.10474063
[138] Härdle W, Mammen E (1993) Comparing nonparametric versus parametric regression fits. Ann Stat 21:1926–1947 · Zbl 0795.62036 · doi:10.1214/aos/1176349403
[139] Härdle W, Marron JS (1990) Semiparametric comparison of regression curves. Ann Stat 18:63–89 · Zbl 0703.62053 · doi:10.1214/aos/1176347493
[140] Härdle W, Mammen E, Müller M (1998) Testing parametric versus semiparametric modeling in generalized linear models. J Am Stat Assoc 93:1461–1474 · Zbl 1064.62543
[141] Härdle W, Sperlich S, Spokoiny V (2001) Structural test in additive regression. J Am Stat Assoc 96:1333–1347 · Zbl 1051.62036 · doi:10.1198/016214501753382264
[142] Hart J (1997) Nonparametric smoothing and lack-of-fit tests. Springer, Berlin · Zbl 0886.62043
[143] Hart J, Wehrly JE (1992) Kernel regression when the boundary region is large, with application to testing the adequacy of polynomial models. J Am Stat Assoc 87:1018–1024 · Zbl 0764.62036 · doi:10.1080/01621459.1992.10476257
[144] He X, Zhu LX (2003) A lack of fit test for quantile regression. J Am Stat Assoc 98:1013–1022 · Zbl 1043.62039 · doi:10.1198/016214503000000963
[145] Henderson PJ, Carroll RJ, Li Q (2008) Nonparametric estimation and testing of fixed effects panel data models. J Econom 144:257–275 · Zbl 1418.62158 · doi:10.1016/j.jeconom.2008.01.005
[146] Heuchenne C, Van Keilegom I (2010) Goodness of fit tests for the error distribution in nonparametric regression. Comput Stat Data Anal 54:1942–1951 · Zbl 1284.62278 · doi:10.1016/j.csda.2010.02.010
[147] Hidalgo J (2008) Specification testing for regression models with dependent data. J Econom 143:143–165 · Zbl 1418.62331 · doi:10.1016/j.jeconom.2007.08.013
[148] Hidalgo J (2009) Goodness of fit for lattice processes. J Econom 151:113–128 · Zbl 1431.62433 · doi:10.1016/j.jeconom.2009.03.003
[149] Hidalgo J, Kreiss JP (2006) Bootstrap specification tests for linear covariance stationary processes. J Econom 133:807–839 · Zbl 1345.62071 · doi:10.1016/j.jeconom.2005.06.015
[150] Hjellvik V, Tjøstheim D (1995) Nonparametric tests of linearity for time series. Biometrika 82:351–368 · Zbl 0823.62044 · doi:10.1093/biomet/82.2.351
[151] Hjellvik V, Tjøstheim D (1996) Nonparametric statistics for testing of linearity and serial independence. J Nonparametr Stat 6:221–251 · Zbl 0880.62049
[152] Hjellvik V, Yao Q, Tjøstheim D (1998) Linearity testing using local polynomial approximation. J Stat Plan Inference 68:295–321 · Zbl 0942.62051 · doi:10.1016/S0378-3758(97)00146-8
[153] Hjort NL, McKeague IW, Van Keilegom I (2009) Extending the scope of empirical likelihood. Ann Stat 37:1079–1111 · Zbl 1160.62029 · doi:10.1214/07-AOS555
[154] Hong Y, Li H (2005) Nonparametric specification testing for continuous-time models with applications to term structure of interest rates. Rev Financ Stud 18:37–84 · doi:10.1093/rfs/hhh006
[155] Horowitz J, Spokoiny V (2001) An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69:599–631 · Zbl 1017.62012 · doi:10.1111/1468-0262.00207
[156] Horowitz J, Spokoiny V (2002) An adaptive, rate-optimal test of linearity for median regression models. J Am Stat Assoc 97:822–835 · Zbl 1048.62050 · doi:10.1198/016214502388618627
[157] Hsiao C, Li Q, Racine JS (2007) A consistent model specification test with mixed discrete and continuous data. J Econom 140:802–826 · Zbl 1247.62126 · doi:10.1016/j.jeconom.2006.07.015
[158] Huang L, Chen J (2008) Analysis of variance, coefficient of determination and f-test for local polynomial regression. Ann Stat 36:2085–2109 · Zbl 1148.62055 · doi:10.1214/07-AOS531
[159] Huang L, Davidson P (2010) Analysis of variance and f-tests for partial linear models with applications to environmental health data. J Am Stat Assoc 105:991–1004 · Zbl 1390.62127 · doi:10.1198/jasa.2010.ap08274
[160] Huskova M, Meintanis S (2007) Omnibus tests for the error distribution in linear regression models. Statistics 41:363–376 · Zbl 1126.62059 · doi:10.1080/02331880701442643
[161] Huskova M, Meintanis S (2009) Goodness-of-fit tests for parametric regression models based on empirical characteristic functions. Kybernetika 45:960–971 · Zbl 1186.62029
[162] Huskova M, Meintanis S (2010) Test for the error distribution in nonparametric possibly heterocedastic regression models. Test 19:92–112 · Zbl 1203.62069 · doi:10.1007/s11749-008-0135-5
[163] Iglesias-Pérez MC, González-Manteiga W (1999) Strong representation of a generalized product-limit estimator for truncated and censored data with some applications. J Nonparametr Stat 10:213–244 · Zbl 1007.62511 · doi:10.1080/10485259908832761
[164] Ingster YI (1982) Minimax nonparametric detection of signals in white Gaussian noise. Probl Inf Transm 18:130–140 · Zbl 0499.94002
[165] Ingster YI (1993a) Asymptotically minimax hypothesis testing for nonparametric alternatives, I. Math Methods Stat 2:85–114 · Zbl 0798.62057
[166] Ingster YI (1993b) Asymptotically minimax hypothesis testing for nonparametric alternatives, II. Math Methods Stat 2:171–189 · Zbl 0798.62058
[167] Ingster YI (1993c) Asymptotically minimax hypothesis testing for nonparametric alternatives, III. Math Methods Stat 2:249–268 · Zbl 0798.62059
[168] Jiménez-Gamero MD, García JM, Pino-Mejías R (2005) Testing goodness of fit for the distribution of errors in multivariate linear models. J Multivar Anal 95:301–322 · Zbl 1070.62029 · doi:10.1016/j.jmva.2004.08.010
[169] Khmadladze EV, Koul HL (2004) Martingale transforms goodness-of-fit tests in regression models. Ann Stat 37:995–1034 · Zbl 1092.62052
[170] Khmadladze EV, Koul HL (2009) Goodness of fit problem for errors in nonparametric regression distribution free approach. Ann Stat 37:3165–3185 · Zbl 1369.62073 · doi:10.1214/08-AOS680
[171] King E, Hart J, Wehrly TE (1991) Testing the equality of two regression curves using linear smoothers. Stat Probab Lett 12:239–247 · doi:10.1016/0167-7152(91)90085-6
[172] Kitamura Y, Tripathi G, Ahn H (2004) Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72:1667–1714 · Zbl 1142.62331 · doi:10.1111/j.1468-0262.2004.00550.x
[173] Koenker P, Basset G (1978) Regression quantiles. Econometrica 46:33–50 · Zbl 0373.62038 · doi:10.2307/1913643
[174] Koul H, Susarla V, Van Ryzin J (1981) Regresssion analysis with randomly right–censored data. Ann Stat 9:1276–1288 · Zbl 0477.62046 · doi:10.1214/aos/1176345644
[175] Koul HL, Ni P (2004) Minimum distance regression model checking. J Stat Plan Inference 119:109–141 · Zbl 1032.62036 · doi:10.1016/S0378-3758(02)00415-9
[176] Koul HL, Sakhanenko L (2005) Goodness of fit testing in regression. A finite sample comparison of bootstrap methodology and Khamaladze transformation. Stat Probab Lett 74:290–302 · Zbl 1070.62030 · doi:10.1016/j.spl.2005.04.053
[177] Koul HL, Song W (2008) Regression model checking with Berkson measurement errors. J Stat Plan Inference 138:1615–1628 · Zbl 1131.62036 · doi:10.1016/j.jspi.2007.05.048
[178] Koul HL, Song W (2009) Minimum distance regression model checking with Berkson measurement errors. Ann Stat 37:132–156 · Zbl 1155.62028 · doi:10.1214/07-AOS565
[179] Koul HL, Song W (2010) Model checking in partial linear regression models with Berkson measurement errors. Stat Sin 20:1551–1579 · Zbl 1200.62037
[180] Koul HL, Stute W (1998) Lack of fit tests in regression with non-random design. Appl Stat Sci 3:53–69
[181] Koul HL, Stute W (1999) Nonparametric model checks for time series. Ann Stat 27:204–236 · Zbl 0955.62089 · doi:10.1214/aos/1018031108
[182] Koul HL, Stute W, Li F (2005) Model diagnosis for setar time series. Stat Sin 15:795–817 · Zbl 1086.62099
[183] Kozek AS (1991) A nonparametric test of fit of a parametric model. J Multivar Anal 37:66–75 · Zbl 0717.62039 · doi:10.1016/0047-259X(91)90111-E
[184] Kreiss JP, Neumann MH, Yao Q (2008) Bootstrap tests for simple structures in nonparametric time series regression. Stat Interface 1:367–380 · Zbl 1230.62049 · doi:10.4310/SII.2008.v1.n2.a13
[185] Kristensen D (2011) Semi-nonparametric estimation and misspecification testing of diffusion models. J Econom 164:382–403 · Zbl 1441.62784 · doi:10.1016/j.jeconom.2011.07.001
[186] Kulasekera KB (1995) Comparison of regression curves using quasi-residuals. J Am Stat Assoc 90:1085–1093 · Zbl 0841.62039 · doi:10.1080/01621459.1995.10476611
[187] Kulasekera KB, Wang J (1997) Smoothing parameter selection for power optimality in testing of regression curves. J Am Stat Assoc 92:500–511 · Zbl 0894.62047 · doi:10.1080/01621459.1997.10474003
[188] Kulasekera KB, Wang J (1998) Bandwidth selection for power optimality in a test of equality of regression curves. Stat Probab Lett 37:287–293 · Zbl 1246.62108 · doi:10.1016/S0167-7152(97)84155-7
[189] Kutoyants YA (2010) On the goodness-of-fit testing for ergodic diffusion processes. J Nonparametr Stat 22:529–543 · Zbl 1189.62138 · doi:10.1080/10485250903359564
[190] Lavergne P (2001) An equality test across nonparametric regressions. Studies in estimation and testing. J Econom 103:307–344 · Zbl 0969.62029 · doi:10.1016/S0304-4076(01)00046-X
[191] Lavergne P, Patilea V (2008) Breaking the curse of dimensionality in nonparametric testing. J Econom 143:103–122 · Zbl 1418.62199 · doi:10.1016/j.jeconom.2007.08.014
[192] Lee S (2006) The Bickel–Rosenblatt test for diffusion processes. Stat Probab Lett 76:1494–1502 · Zbl 1095.62099 · doi:10.1016/j.spl.2006.03.009
[193] Lee S, Na S (2002) On the Bickel-Rosenblatt test for first-order autoregressive models. Stat Probab Lett 56:23–25 · Zbl 0994.62082 · doi:10.1016/S0167-7152(01)00143-2
[194] Lee S, Wee IS (2008) Residual empirical process for difussion processes. J Korean Math Soc 45:683–693 · Zbl 1140.60337 · doi:10.4134/JKMS.2008.45.3.683
[195] Li CS (2005) Using local linear kernel smoothers to test the lack of fit of nonlinear regression models. Stat Methodol 2:267–284 · Zbl 1248.62056 · doi:10.1016/j.stamet.2005.06.001
[196] Li F (2007) Testing the parametric specification of the diffusion function in a difussion process. Econom Theory 23:221–250 · Zbl 1237.62102
[197] Li F, Tkacz G (2006) A consistent bootstrap test for conditional density functions with time-series data. J Econom 133:863–886 · Zbl 1345.62073 · doi:10.1016/j.jeconom.2005.06.016
[198] Li Q, Wang S (1998) A simple consistent bootstrap test for a parametric regression functional form. J Econom 87:145–165 · Zbl 0943.62031 · doi:10.1016/S0304-4076(98)00011-6
[199] Li X (2012) Lack of fit testing of a regression model with response missing at random. J Stat Plan Inference 142:155–170 · Zbl 1227.62027 · doi:10.1016/j.jspi.2011.07.005
[200] Liang HY, Jing BY (2007) The LIL for the Bickel-Rosenblatt test statistic. J Stat Plan Inference 137:1829–1837 · Zbl 1113.62039 · doi:10.1016/j.jspi.2006.06.036
[201] Liang HY, Liu X, Li R, Tsai C (2010) Estimation and testing for partially linear single index model. Ann Stat 38:3811–3836 · Zbl 1204.62068 · doi:10.1214/10-AOS835
[202] Liero H (2003) Testing homocedasticity in nonparametric regression. J Nonparametr Stat 15:31–51 · Zbl 1019.62036 · doi:10.1080/10485250306038
[203] Liero H, Läuter H, Konakov V (1998) Nonparametric versus parametric goodness of fit. Statistics 31:115–149 · Zbl 0952.62045 · doi:10.1080/02331889808802632
[204] Lin W, Kulasekera KB (2010) Testing the equality of linear single-index models. J Multivar Anal 101:1156–1167 · Zbl 1185.62076 · doi:10.1016/j.jmva.2009.10.006
[205] Liu R (1988) Bootstrap procedures under some non-i.i.d. models. Ann Stat 16:1696–1708 · Zbl 0655.62031 · doi:10.1214/aos/1176351062
[206] Liu Z, Stengos T, Li Q (2000) Nonparametric model check based on local polynomial fitting. Stat Probab Lett 48:327–334 · Zbl 0982.62037 · doi:10.1016/S0167-7152(00)00012-2
[207] Lombardía MJ, Sperlich S (2008) Semiparametric inference in generalized mixed effect models. J R Stat Soc B 70:913–930 · doi:10.1111/j.1467-9868.2008.00655.x
[208] Lopez O, Patilea V (2009) Nonparametric lack-of-fit tests for parametric mean–regression models with censored data. J Multivar Anal 100:210–230 · Zbl 1151.62036 · doi:10.1016/j.jmva.2008.04.008
[209] Ma Y, Hart JD, Janicki R, Carroll RJ (2011) Local and omnibus goodness-of-fit tests in classical measurement error models. J R Stat Soc B 73:81–98 · doi:10.1111/j.1467-9868.2010.00751.x
[210] Maity A, Carroll RJ, Mammen E, Chatterjee W (2009) Testing in semiparametric models with interaction, with applications to genenvironment interactions. J R Stat Soc B 71:75–96 · Zbl 05691132 · doi:10.1111/j.1467-9868.2008.00671.x
[211] Masuda H, Negri I, Nishiyama Y (2010) Goodness-of-fit test for ergodic diffusions by discrete–time observation: an innovation martingale approach. J Nonparametr Stat 23:237–254 · Zbl 1359.62149 · doi:10.1080/10485252.2010.510186
[212] McKeague IW, Zhang MJ (1994) Identification of nonlinear time series from first order cummulative characteristics. Ann Stat 22:495–514 · Zbl 0797.62073 · doi:10.1214/aos/1176325381
[213] Meintanis SG, Portnoy S (2011) Specification tests in mixed effects models. J Stat Plan Inference 141:2545–2555 · Zbl 1213.62119 · doi:10.1016/j.jspi.2011.02.004
[214] Miles D, Mora J (2002) On the performance of nonparametric specification test in regression models. Comput Stat Data Anal 42:477–490 · Zbl 1429.62161 · doi:10.1016/S0167-9473(02)00227-X
[215] Monsalve-Cobis A, González-Manteiga W, Febrero-Bande M (2011) Goodness-of-fit tests for interest rate models: an approach based on empirical processes. Comput Stat Data Anal 55:3073–3092 · Zbl 1262.91154 · doi:10.1016/j.csda.2011.06.004
[216] Mora J (2005) Comparing distribution functions of errors in linear models: a nonparametric approach. Stat Probab Lett 73:425–432 · Zbl 1071.62036 · doi:10.1016/j.spl.2005.04.017
[217] Mora J, Pérez-Alonso A (2009) Specification tests for the distribution of errors in nonparametric regression: a martingale approach. J Nonparametr Stat 21:441–452 · Zbl 1161.62019 · doi:10.1080/10485250802666192
[218] Müller HG (1992) Goodness-of-fit diagnostics for regression models. Scand J Stat 19:157–172 · Zbl 0760.62037
[219] Müller M (2001) Estimation and testing in generalized partial linear models–a comparative study. Stat Comput 11:299–399 · doi:10.1023/A:1011981314532
[220] Müller UU, Shick A, Welfemeyer W (2009) Estimating the error distribution function in nonparametric regression with multivariate covariates. Stat Probab Lett 79:957–964 · Zbl 1158.62032 · doi:10.1016/j.spl.2008.11.024
[221] Munk A, Dette H (1998) Nonparametric comparison of several regression functions: exact and asymptotic theory. Ann Stat 6:2339–2368 · Zbl 0927.62040
[222] Munk A, Neumeyer N, Scholz A (2007) Non-parametric analysis of covariance. The case of inhomogeneous and heteroscedastic noise. Scand J Stat 34:511–534 · Zbl 1150.62022 · doi:10.1111/j.1467-9469.2006.00535.x
[223] Nadaraya EA (1964) On estimating regression. Theory Probab Appl 10:186–196 · Zbl 0134.36302 · doi:10.1137/1110024
[224] Negri I, Nishiyama Y (2009) Goodness-of-fit test for ergodic diffusion process. Ann Inst Math Stat 61:167–198 · Zbl 1332.62301
[225] Negri I, Nishiyama Y (2010) Goodness-of-fit test for ergodic diffusion process by tick time sample scheme. Statistical inference for stochastic processes, vol 13, pp 81–95 · Zbl 1205.62115
[226] Neumann MH, Paparoditis E (2000) On bootstrapping l 2-statistics in density testing. Stat Probab Lett 50:137–147 · Zbl 0966.62029 · doi:10.1016/S0167-7152(00)00091-2
[227] Neumann MH, Paparoditis E (2008a) Simultaneous confidence bands in spectral density estimation. Biometrika 95:381–397 · Zbl 1437.62563 · doi:10.1093/biomet/asn005
[228] Neumann MH, Paparoditis E (2008b) Goodness-of-fit tests for Markovian time series models: central limit theory and bootstrap approximations. Bernoulli 14:14–46 · Zbl 1155.62058 · doi:10.3150/07-BEJ6055
[229] Neumeyer N (2009) Smooth residual bootstrap for empirical processes of nonparametric regression residuals. Scand J Stat 36:204–228 · Zbl 1194.62051 · doi:10.1111/j.1467-9469.2008.00628.x
[230] Neumeyer N, Dette H (2003) Nonparametric comparison of regression curves: an empirical process approach. Ann Stat 31:880–920 · Zbl 1032.62037 · doi:10.1214/aos/1056562466
[231] Neumeyer N, Sperlich S (2006) Comparison of separable components in different samples. Scand J Stat 33:444–501 · Zbl 1114.62054
[232] Neumeyer N, Van Keilegom I (2010) Estimating the error distribution in nonparametric multiple regression with applications to model testing. J Multivar Anal 101:1067–1078 · Zbl 1185.62078 · doi:10.1016/j.jmva.2010.01.007
[233] Ojeda JL, Van Keilegom I (2009) Goodness-of-fit tests for parametric regression with selection biased data. J Stat Plan Inference 139:2836–2850 · Zbl 1162.62031 · doi:10.1016/j.jspi.2009.01.008
[234] Ojeda JL, Cristóbal JA, Alcalá JT (2008) A bootstrap approach to model checking for linear models under length-biased data. Ann Inst Math Stat 60:519–543 · Zbl 1169.62310 · doi:10.1007/s10463-006-0111-3
[235] Ojeda JL, González-Manteiga W, Cristóbal JA (2011) A bootstrap based model checking for selection-biased data. Technical report, University of Santiago de Compostela
[236] Owen A (2001) Empirical likelihood. Chapman & Hall, New York
[237] Pan Z, Lin DY (2005) Goodness-of-fit methods for generalized linear mixed models. Biometrics 61:1000–1009 · Zbl 1087.62081 · doi:10.1111/j.1541-0420.2005.00365.x
[238] Paparoditis E (2000) Spectral density based goodness-of-fit tests for time series models. Scand J Stat 27:143–176 · Zbl 0940.62084 · doi:10.1111/1467-9469.00184
[239] Paparoditis E (2009) Testing temporal constancy of the spectral structure of a time series. Bernoulli 15:1190–1221 · Zbl 1200.62049 · doi:10.3150/08-BEJ179
[240] Paparoditis E (2010) Validating stationary assumptions in time series analysis by rolling local periodograms. J Am Stat Assoc 105:839–851 · Zbl 1392.62275 · doi:10.1198/jasa.2010.tm08243
[241] Pardo-Fernández JC (2007) Comparison of error distributions in nonparametric regression. Stat Probab Lett 77:350–356 · Zbl 1106.62044 · doi:10.1016/j.spl.2006.07.015
[242] Pardo-Fernández JC, Van Keilegom I (2006) Comparison of regression curves with censored responses. Scand J Stat 33:409–434 · Zbl 1115.62041 · doi:10.1111/j.1467-9469.2006.00508.x
[243] Pardo-Fernández JC, Van Keilegom I, González-Manteiga W (2007a) Goodness-of-fit tests for parametric models in censored regression. Can J Stat 35:249–264 · Zbl 1129.62036 · doi:10.1002/cjs.5550350204
[244] Pardo-Fernández JC, Van Keilegom I, González-Manteiga W (2007b) Testing for the equality of k regression curves. Stat Sin 17:1115–1137 · Zbl 1133.62031
[245] Park C, Kang K (2008) Sizer analysis for the comparison of regression curves. Comput Stat Data Anal 52:3954–3970 · Zbl 1452.62291 · doi:10.1016/j.csda.2008.01.006
[246] Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065–1076 · Zbl 0116.11302 · doi:10.1214/aoms/1177704472
[247] Priestley MB, Chao MT (1972) Non-parametric function fitting. J R Stat Soc B 34:385–392 · Zbl 0263.62044
[248] Ramil-Novo LA, González-Manteiga W (1998) \(\chi\) 2 goodness-of-fit tests for polynomial regression. Commun Stat, Simul Comput 27:229–258 · Zbl 0893.62029 · doi:10.1080/03610919808813477
[249] Ramil-Novo LA, González-Manteiga W (2000) F tests and regression analysis of variance based on smoothing splines estimators. Stat Sin 10:819–837 · Zbl 0952.62037
[250] Ramsay J, Silverman B (2005) Functional data analysis. Springer, New York · Zbl 1079.62006
[251] Raz J (1990) Testing for no effect when estimating a smooth function by nonparametric regression: a randomization approach. J Am Stat Assoc 85:132–138 · doi:10.1080/01621459.1990.10475316
[252] Robinson PM (1988) Root-N-consistent semiparametric regression. Econometrica 56:931–944 · Zbl 0647.62100 · doi:10.2307/1912705
[253] Roca-Pardiñas J, Sperlich S (2007) Testing the link when the index is semiparametric. a comparative study. Comput Stat Data Anal 51:6365–6581 · Zbl 1445.62093
[254] Roca-Pardiñas J, Cadarso-Suárez C, González-Manteiga W (2005) Testing for interactions in generalized additive models: application to ${\(\backslash\)rm SO}\(\backslash\)sb{2}$ pollution data. Stat Comput 15:289–299 · doi:10.1007/s11222-005-4072-9
[255] Rodríguez-Campos C, González-Manteiga W, Cao R (1998) Testing the hypothesis of a generalized linear regression model using nonparametric regression estimation. J Stat Plan Inference 67:99–122 · Zbl 0932.62052 · doi:10.1016/S0378-3758(97)00098-0
[256] Rosenblatt M (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832–837 · Zbl 0073.14602 · doi:10.1214/aoms/1177728190
[257] Rosenblatt M (1991) Stochastic curve estimation. Institute of Mathematical Statistics, Hayward · Zbl 1163.62318
[258] Samarakoon N, Song W (2010) Minimum distance conditional variance function checking in heteroscedastic regression models. J Multivar Anal 102:579–600 · Zbl 1207.62090 · doi:10.1016/j.jmva.2010.11.003
[259] Samarov A (1993) Exploring regression structure using nonparametric functional estimation. J Am Stat Assoc 88:836–847 · Zbl 0790.62035 · doi:10.1080/01621459.1993.10476348
[260] Sánchez BN, Houseman EA, Ryan LM (2009) Residual-based diagnostics for structural equation models. Biometrics 65:104–115 · Zbl 1159.62341 · doi:10.1111/j.1541-0420.2008.01022.x
[261] Sánchez-Sellero C, González-Manteiga W, Van Keilegom I (2005) Uniform representation of product–limit integrals with applications. Scand J Stat 32:563–581 · Zbl 1092.62027 · doi:10.1111/j.1467-9469.2005.00453.x
[262] Seber GAF (1977) Linear regression analysis. Wiley, New York · Zbl 0354.62055
[263] Seber GAF, Wild CG (1989) Nonlinear regression. Wiley, New York
[264] Sergides M, Paparoditis E (2007) Bootstrapping the local periodogram of locally stationary processes. J Time Ser Anal 29:264–279 · Zbl 1164.62062 · doi:10.1111/j.1467-9892.2007.00556.x
[265] Sergides M, Paparoditis E (2009) Frequency domain tests of semiparametric hypotheses for locally stationary processes. Scand J Stat 36:800–821 · Zbl 1224.62070 · doi:10.1111/j.1467-9469.2009.00652.x
[266] Song K (2010) Testing semiparametric conditional moment restrictions using conditional martingale transforms. J Econom 154:74–84 · Zbl 1431.62199 · doi:10.1016/j.jeconom.2009.07.002
[267] Song W (2008) Model checking in errors-in-variables regression. J Multivar Anal 99:2406–2443 · Zbl 1151.62033 · doi:10.1016/j.jmva.2008.02.034
[268] Song Z (2011) A martingale approach for testing diffusion models based on infinitesimal operator. J Econom 162:189–212 · Zbl 1441.62873 · doi:10.1016/j.jeconom.2010.12.005
[269] Speckman P (1988) Kernel smoothing in partial linear models. J R Stat Soc B 50:413–436 · Zbl 0671.62045
[270] Sperlich S, Lombardía MJ (2010) Local polynomical inference for small area statistics: estimation, validation and prediction. J Nonparametr Stat 22:633–648 · Zbl 1327.62268 · doi:10.1080/10485250903311607
[271] Sperlich S, Linton O, Härdle W (1999) Integration and backfitting methods in additive models: finite sample properties and comparison. Test 8:419–458 · Zbl 0938.62045 · doi:10.1007/BF02595879
[272] Sperlich S, Tjøstheim D, Yang L (2002) Nonparametric estimation and testing of interaction in additive models. Econom Theory 18:197–251 · Zbl 1109.62310
[273] Spokoiny V (1996) Adaptive hypothesis testing using wavelets. Ann Stat 24:2477–2498 · Zbl 0898.62056 · doi:10.1214/aos/1032181163
[274] Spokoiny V (2001) Data driven testing the fit of linear models. Math Methods Stat 10:465–497 · Zbl 1006.62043
[275] Srihera R, Stute W (2010) Nonparametric comparison of regression functions. J Multivar Anal 101:2039–2059 · Zbl 1194.62056 · doi:10.1016/j.jmva.2010.05.001
[276] Staniswalis JG, Severini TA (1991) Diagnostics for assessing regression models. J Am Stat Assoc 86:684–692 · Zbl 0736.62063 · doi:10.1080/01621459.1991.10475095
[277] Stute W (1993) Consistent estimation under random censorship when covariables are present. J Multivar Anal 45:89–103 · Zbl 0767.62036 · doi:10.1006/jmva.1993.1028
[278] Stute W (1996) Distributional convergence under random censorship when covariables are present. Scand J Stat 23:461–471 · Zbl 0903.62045
[279] Stute W (1997) Nonparametric model checks for regression. Ann Stat 25:613–641 · Zbl 0926.62035 · doi:10.1214/aos/1031833666
[280] Stute W (1999) Nonlinear censored regression. Stat Sin 25:613–641 · Zbl 0940.62061
[281] Stute W, González-Manteiga W (1996) Nn goodness-of-fit tests for linear models. J Stat Plan Inference 53:75–92 · Zbl 0847.62036 · doi:10.1016/0378-3758(95)00144-1
[282] Stute W, Zhu L (2005a) Nonparametric checks for single–index models. Ann Stat 33:1048–1083 · Zbl 1080.62023 · doi:10.1214/009053605000000020
[283] Stute W, Zhu L (2005b) Model checks for generalized linear models. Scand J Stat 29:535–545 · Zbl 1035.62073 · doi:10.1111/1467-9469.00304
[284] Stute W, González-Manteiga W, Presedo-Quindimil MA (1993) Boostrap based goodness-of-fit tests. Metrika 40:243–256 · Zbl 0770.62016 · doi:10.1007/BF02613687
[285] Stute W, González-Manteiga W, Presedo-Quindimil M (1998a) Bootstrap approximations in model checks for regression. J Am Stat Assoc 93:141–149 · Zbl 0902.62027 · doi:10.1080/01621459.1998.10474096
[286] Stute W, Thies S, Zhu LX (1998b) Model checks for regression: an innovation process approach. Ann Stat 26:1916–1934 · Zbl 0930.62044 · doi:10.1214/aos/1024691363
[287] Stute W, González-Manteiga W, Sánchez-Sellero C (2000) Nonparametric model checks in censored regression. Commun Stat, Theory Methods 29:1611–1629 · Zbl 1018.62030 · doi:10.1080/03610920008832568
[288] Stute W, Presendo-Quindimil M, González-Manteiga W, Koul HL (2006) Model checks for higher order time series. Stat Probab Lett 76:1385–1396 · Zbl 1094.62117 · doi:10.1016/j.spl.2006.02.009
[289] Stute W, Xu WL, Zhu X (2008) Model diagnosis for parametric regression in high–dimensional spaces. Biometrika 95:451–467 · Zbl 1437.62614 · doi:10.1093/biomet/asm095
[290] Su JQ, Wei LJ (1991) A lack of fit test for the mean function in a generalized linear model. J Am Stat Assoc 86:420–426 · doi:10.1080/01621459.1991.10475059
[291] Sun Y (2006) A consistent nonparametric equality test of conditional quantile functions. Econom Theory 22:614–632 · Zbl 1108.62316
[292] Sun Z, Wang Q (2009) Checking the adequacy of a general linear model with responses missing at random. J Stat Plan Inference 139:3588–3604 · Zbl 1167.62037 · doi:10.1016/j.jspi.2009.04.024
[293] Sun Z, Wang Q, Dai P (2009) Model checking for partially linear models with missing responses at random. J Multivar Anal 100:636–651 · Zbl 1163.62032 · doi:10.1016/j.jmva.2008.07.002
[294] Tenreiro C (2007) On the asymptotic behaviour of location-scale invariant Bickel-Rosenblatt tests. J Stat Plan Inference 137:103–116. Erratum, no 139:2115 · Zbl 1098.62055 · doi:10.1016/j.jspi.2005.11.006
[295] Tenreiro C (2009) On the choice of the smoothing parameter for the bhep goodness-of-fit test. Comput Stat Data Anal 53:1038–1053 · Zbl 1452.62322 · doi:10.1016/j.csda.2008.09.002
[296] Teodorescu B, Van Keilegom I (2010) A goodness-of-fit test for generalized conditional linear models under left truncation and right censoring. J Nonparametr Stat 22:547–566 · Zbl 1263.62084 · doi:10.1080/10485250903302788
[297] Teodorescu B, Van Keilegom I, Cao R (2010) Generalized conditional linear models under left truncation and right censoring. Ann Inst Math Stat 62:465–485 · Zbl 1263.62084 · doi:10.1007/s10463-008-0187-z
[298] Tripathi G, Kitamura Y (2003) Testing conditional moment restrictions. Ann Stat 31:2059–2095 · Zbl 1044.62049 · doi:10.1214/aos/1074290337
[299] Van Keilegom I, González-Manteiga W, Sánchez-Sellero C (2008a) Goodness-of-fit tests in parametric regression based on the estimation of the error distribution. Test 17:401–415 · Zbl 1196.62049 · doi:10.1007/s11749-007-0044-z
[300] Van Keilegom I, Sánchez-Sellero C, González-Manteiga W (2008b) Empirical likelihood based testing for regression. Electron J Stat 2:581–604 · Zbl 1320.62034 · doi:10.1214/07-EJS152
[301] Vilar-Fernández JM, González-Manteiga W (1996) Bootstrap test of goodness of fit to a linear model when errors are correlated. Commun Stat, Theory Methods 25:2925–2953 · Zbl 0870.62037 · doi:10.1080/03610929608831879
[302] Vilar-Fernández JM, González-Manteiga W (2000) Resampling for checking linear regression models via non-parametric regression estimation. Comput Stat Data Anal 35:211–231 · Zbl 0967.62025 · doi:10.1016/S0167-9473(99)00117-6
[303] Vilar-Fernández JM, González-Manteiga W (2004) Nonparametric comparison of curves with dependent errors. Statistics 38:81–99 · doi:10.1080/02331880310001634656
[304] Vilar-Fernández JM, Vilar-Fernández JA, González-Manteiga W (2007) Bootstrap tests for nonparametric comparison of regression curves with dependent errors. Test 16:123–144 · Zbl 1119.62033 · doi:10.1007/s11749-006-0005-y
[305] Wang L (2008) Nonparametric test for checking lack of fit of the quantile regression model under random censoring. Can J Stat 36:321–336 · Zbl 1144.62032 · doi:10.1002/cjs.5550360209
[306] Watson GS (1964) Smooth regression analysis. Sankhyā Ser A 26:359–372 · Zbl 0137.13002
[307] Wong H, Liu F, Chen M, Cheung IW (2009) Empirical likelihood based diagnostics for heteroscedasticity in partial linear models. Comput Stat Data Anal 53:3466–3477 · Zbl 1453.62246 · doi:10.1016/j.csda.2009.02.029
[308] Wooldridge JM (1992) A test for functional form against nonparametric alternatives. Econom Theory 4:935–955 · Zbl 0781.62100
[309] Wu CFJ (1986) Jackknife, bootstrap and other resampling methods in regression analysis. Ann Stat 14:1261–1350 · Zbl 0618.62072 · doi:10.1214/aos/1176350142
[310] Xia Y (2009) Model checking in regression via dimension reduction. Biometrica 96:133–148 · Zbl 1162.62036 · doi:10.1093/biomet/asn074
[311] Xia Y, Li WK, Tong H, Zhang D (2004) A goodness-of-fit test for single-index models. Stat Sin 14:1–39 · Zbl 1040.62034
[312] You J, Chen G (2005) Testing heteroscedasticity in partially linear regression models. Stat Probab Lett 73:61–70 · Zbl 1101.62033 · doi:10.1016/j.spl.2005.03.002
[313] Young S, Bowman AW (1995) Non–parametric analysis of covariance. Biometrics 51:920–931 · Zbl 0875.62312 · doi:10.2307/2532993
[314] Zhang C (2003) Calibrating the degrees of freedom for automatic data smoothing and effective curve checking. J Am Stat Assoc 98:609–629 · Zbl 1040.62027 · doi:10.1198/016214503000000521
[315] Zhang C (2004) Assessing the equivalence of nonparametric regression tests based on spline and local polynomial smoothers. J Stat Plan Inference 126:73–95 · Zbl 1072.62032 · doi:10.1016/j.jspi.2003.07.013
[316] Zhang C, Dette H (2004) A power comparison between nonparametric regression tests. Stat Probab Lett 66:289–301 · Zbl 1102.62049 · doi:10.1016/j.spl.2003.11.005
[317] Zheng JX (1996) A consistent test of functional form via nonparametric estimation techniques. J Econom 75:263–289 · Zbl 0865.62030 · doi:10.1016/0304-4076(95)01760-7
[318] Zheng JX (1998) A consistent nonparametric test of parametric regression models under conditional quantile restrictions. Econom Theory 14:123–138
[319] Zhou Z (2010) Nonparametric inference of quantile curves for nonstationary time series. Ann Stat 38:2187–2217 · Zbl 1202.62062 · doi:10.1214/09-AOS769
[320] Zhu H, Ibrahim JG, Shi X (2009) Diagnostic measures for generalized linear models with missing covariates. Scand J Stat 36:686–712 · Zbl 1224.62017 · doi:10.1111/j.1467-9469.2009.00644.x
[321] Zhu L (2005) Nonparametric Monte Carlo tests and their applications. Lecture notes in statistics, vol 182. Springer, Berlin · Zbl 1094.62058
[322] Zhu L, Ng KW (2003) Checking the adequacy of a partial linear model. Stat Sin 13:763–781 · Zbl 1028.62032
[323] Zhu L, Fujikoshi Y, Naito K (2001) Heteroscedasticity checks for regression models. Sci China 44:1236–1252 · Zbl 0995.62041 · doi:10.1007/BF02877011
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