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Specification tests in semiparametric transformation models — a multiplier bootstrap approach. (English) Zbl 07178853
Summary: Semiparametric transformation models are considered, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. Subsequent procedures for testing lack-of-fit of the regression function and for significance of covariates are suggested. In contrast to existing procedures, the tests are asymptotically not influenced by the pre-estimation of the transformation in the sense that they have the same asymptotic distribution as in regression models without transformation. Validity of a multiplier bootstrap procedure is shown which is easier to implement and much less computationally demanding than bootstrap procedures based on the transformation model. In a simulation study the superior performance of the procedure in comparison with its existing competitors is demonstrated.
MSC:
62-XX Statistics
Software:
R
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[1] Alcalá, J. T.; Cristóbal, J. A.; González-Manteiga, W., Goodness-of-fit test for linear models based on local polynomials, Statist. Probab. Lett., 42, 39-46 (1999) · Zbl 0946.62016
[2] Allison, J. S.; Hušková, M.; Meintanis, S. G., Testing the adequacy of semiparametric transformation models, TEST, 27, 70-94 (2018) · Zbl 1386.62012
[3] Bickel, P.; Doksum, K. A., An analysis of transformations revisited, J. Amer. Statist. Assoc., 76, 296-311 (1981) · Zbl 0464.62058
[4] Bierens, H. J., Consistent model specification tests, J. Econometrics, 20, 105-134 (1982) · Zbl 0549.62076
[5] Box, G. E.P.; Cox, D. R., An analysis of transformations, J. R. Stat. Soc. Ser. B Stat. Methodol., 26, 211-252 (1964) · Zbl 0156.40104
[6] Bücher, A.; Dette, H., Multiplier bootstrap of tail copulas with applications, Bernoulli, 19, 1655-1687 (2013) · Zbl 1281.62124
[7] Colling, B.; Van Keilegom, I., Goodness-of-fit tests in semiparametric transformation models, TEST, 25, 291-308 (2016), online supplementary material available · Zbl 1342.62058
[8] Colling, B.; Van Keilegom, I., Goodness-of-fit tests in semiparametric transformation models using the integrated regression function, J. Multivariate Anal., 160, 10-30 (2017) · Zbl 1373.62190
[9] Colling, B.; Van Keilegom, I., Estimation of a Semiparametric Transformation Model: A Novel Approach Based on Least Squares Minimization (2018), KU Leuven, preprint available at https://limo.libis.be/primo-explore/search?vid=Lirias
[10] Emura, T.; Konno, Y., A goodness-of-fit tests for parametric models based on dependently truncated data, Comput. Statist. Data Anal., 56, 2237-2250 (2012) · Zbl 1252.62052
[11] Escanciano, J. C., A consistent diagnostic test for regression models using projections, Econometric Theory, 22, 1030-1051 (2006) · Zbl 1170.62318
[12] Fan, J.; Gijbels, I., (Local Polynomial Modelling and Its Applications. Local Polynomial Modelling and Its Applications, Monographs on Statistics and Applied Probability (1996), Chapman & Hall: Chapman & Hall New York) · Zbl 0873.62037
[13] Fan, Y.; Li, Q., Consistent model specification tests: omitted variables and semiparametric functional forms, Econometrica, 64, 865-890 (1996) · Zbl 0854.62038
[14] Genest, C.; Rémillard, B., Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models, Ann. Inst. Henri Poincaré Probab. Stat., 44, 1096-1127 (2008) · Zbl 1206.62044
[15] González-Manteiga, W.; Crujeiras, R. M., An updated review of goodness-of-fit tests for regression models, TEST, 22, 361-411 (2013), With discussion · Zbl 1273.62086
[16] Hall, P.; Heyde, C. C., Martingale Limit Theory and Its Application (1980), Academic Press: Academic Press New York · Zbl 0462.60045
[17] Härdle, W.; Mammen, E., Comparing nonparametric versus parametric regression fits, Ann. Statist., 21, 1926-1947 (1993) · Zbl 0795.62036
[18] Heckert, N. A.; Filliben, J. J.; Croarkin, C. M.; Hembree, B.; Guthrie, W. F.; Tobias, P.; Prinz, J., NIST/SEMATECH e-Handbook of Statistical Methods (2002), available at https://www.itl.nist.gov/div898/handbook/pmd/section6/pmd631htm
[19] Hinkley, D. V.; Runger, G., The analysis of transformed data, J. Amer. Statist. Assoc., 79, 302-320 (1984), With discussion · Zbl 0553.62051
[20] Hlávka, Z.; Hušková, M.; Kirch, C.; Meintanis, S. G., Fourier-type tests involving martingale difference processes, Econometric Rev., 36, 468-492 (2017)
[21] Horowitz, J. L., Semiparametric estimation of a regression model with an unknown transformation of the dependent variable, Econometrica, 64, 102-137 (1996) · Zbl 0861.62029
[22] Kojadinovic, I.; Yan, J.; Holmes, M., Fast large-sample goodness-of-fit tests for copulas, Statist. Sinica, 21, 841-871 (2011) · Zbl 1214.62049
[23] Lavergne, P.; Maistre, S.; Patilea, V., A significance test for covariates in nonparametric regression, Electron. J. Stat., 9, 643-678 (2015) · Zbl 1309.62076
[24] Lavergne, P.; Vuong, Q., Nonparametric significance testing, Econometric Theory, 16, 576-601 (2000) · Zbl 0968.62047
[25] Lin, D. Y.; Wei, L. J.; Ying, Z., Model-checking techniques based on cumulative residuals, Biometrics, 58, 1-12 (2002) · Zbl 1209.62168
[26] Linton, O.; Chen, R.; Wang, N.; Härdle, W., An analysis of transformations for additive nonparametric regression, J. Amer. Statist. Assoc., 92, 1512-1521 (1997) · Zbl 0912.62048
[27] Linton, O.; Sperlich, S.; Van Keilegom, I., Estimation on a semiparametric transformation model, Ann. Statist., 36, 686-718 (2008) · Zbl 1133.62029
[28] Nadaraya, E. A., On estimating regression, Theory Probab. Appl., 9, 141-142 (1964) · Zbl 0136.40902
[29] Neumeyer, N.; Noh, H.; Van Keilegom, I., Heteroscedastic semiparametric transformation models: estimation and testing for validity, Statistica Sinica, 26, 925-954 (2016) · Zbl 1360.62189
[30] R Core Team, R: A Language and Environment for Statistical Computing (2017), R Foundation for Statistical Computing: R Foundation for Statistical Computing Vienna, Austria, URL http://www.R-project.org/
[31] Silverman, B. W., Density Estimation for Statistics and Data Analysis (1986), Chapman and Hall · Zbl 0617.62042
[32] Spokoiny, V.; Zhilova, M., Bootstrap confidence sets under model misspecification, Ann. Statist., 43, 2653-2675 (2015) · Zbl 1327.62179
[33] Stute, W., Nonparametric model checks for regression, Ann. Statist., 25, 613-641 (1997) · Zbl 0926.62035
[34] van der Vaart, A. W., Asymptotic Statistics (1998), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0910.62001
[35] van der Vaart, A. W.; Wellner, J. A., Weak Convergence and Empirical Processes (1996), Springer-Verlag: Springer-Verlag New York · Zbl 0862.60002
[36] Van Keilegom, I.; González-Manteiga, W.; Sánchez Sellero, C., Goodness of fit tests in parametric regression based on the estimation of the error distribution, TEST, 17, 401-415 (2008) · Zbl 1196.62049
[37] Watson, G. S., Smooth regression analysis, Sankhya A, 26, 359-372 (1964) · Zbl 0137.13002
[38] Wu, C. F.J., Jackknife, bootstrap and other resampling methods in regression analysis, Ann. Statist., 14, 1261-1350 (1986) · Zbl 0618.62072
[39] Yeo, I.-K.; Johnson, R. A., A new family of power transformations to improve normality or symmetry, Biometrika, 87, 954-959 (2000) · Zbl 1028.62010
[40] Zellner, A.; Revankar, N. S., Generalized production functions, Rev. Econ. Stud., 36, 241-250 (1969) · Zbl 0176.50103
[41] Zheng, J. X., A consistent test of functional form via nonparametric estimation techniques, J. Econometrics, 75, 263-289 (1996) · Zbl 0865.62030
[42] Zhu, L.; Fujikoshi, N.; Naito, K., Heteroscedasticity checks for regression models, Sci. China A, 44, 1237-1252 (2001) · Zbl 0995.62041
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