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Specification analysis of linear quantile models. (English) Zbl 1293.62097
Summary: This paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels. These tests may be applied to assess the validity of post-estimation inferences regarding the effect of conditioning variables on the distribution of outcomes. We show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure. Monte Carlo evidence and an application to the empirical analysis of age-earnings curves are included.

62G10 Nonparametric hypothesis testing
62P20 Applications of statistics to economics
91B82 Statistical methods; economic indices and measures
Full Text: DOI
[1] Angrist, J.; Chernozhukov, V.; Fernández-Val, I., Quantile regression under misspecification, with an application to the US wage structure, Econometrica, 74, 539-563, (2006) · Zbl 1145.62399
[2] Beran, R.; Ducharme, G. R., Asymptotic theory for bootstrap methods in statistics, (1991), Les Publications du Centre de Recherches Mathématiques Montreal · Zbl 0733.62050
[3] Bickel, P. J.; Ritov, Y.; Stoker, T. M., Tailor-made tests for goodness of fit to semiparametric hypotheses, Annals of Statistics, 34, 721-741, (2006) · Zbl 1092.62050
[4] Bierens, H. J., Consistent model specification tests, Journal of Econometrics, 20, 105-134, (1982) · Zbl 0549.62076
[5] Bierens, H. J.; Ginther, D. K., Integrated conditional moment testing of quantile regression models, Empirical Economics, 26, 307-324, (2001)
[6] Bilias, Y.; Chen, S.; Ying, Z., Simple resampling methods for censored regression quantiles, Journal of Econometrics, 99, 373-386, (2000) · Zbl 1076.62567
[7] Chang, N. M., Weak convergence of a self-consistent estimator of a survival function with doubly censored data, Annals of Statistics, 18, 391-404, (1990) · Zbl 0706.62044
[8] Chen, X.; Linton, O.; van Keilegom, I., Estimation of semiparametric models when the criterion function is not smooth, Econometrica, 71, 1591-1608, (2003) · Zbl 1154.62325
[9] Chernozhukov, V.; Fernández-Val, I., Subsampling inference on quantile regression processes, Sankhyā, 67, 253-276, (2005) · Zbl 1192.62128
[10] Chernozhukov, V.; Hansen, C., An IV model of quantile treatment effects, Econometrica, 73, 245-262, (2005) · Zbl 1152.91706
[11] Choi, S.; Hall, W. J.; Schick, A., Asymptotically uniformly most powerful tests in parametric and semiparametric models, Annals of Statistics, 24, 841-861, (1996) · Zbl 0860.62020
[12] Dudley, R. M., Uniform central limit theorems, (1999), Cambridge University Press Cambridge, UK · Zbl 0951.60033
[13] Escanciano, J.C., Goh, C., 2012. Conditional density estimation in linear quantile regression (unpublished paper).
[14] Escanciano, J.C., Jacho-Chávez, D.T., Lewbel, A., 2013. Uniform convergence of weighted sums of non- and semi-parametric residuals for estimation and testing. Journal of Econometrics (forthcoming). Supplemental materials. · Zbl 1293.62106
[15] Escanciano, J. C.; Velasco, C., Specification tests of parametric dynamic conditional quantiles, Journal of Econometrics, 159, 209-221, (2010) · Zbl 1431.62186
[16] Gutenbrunner, C.; Jurečková, J., Regression rank scores and regression quantiles, Annals of Statistics, 20, 305-330, (1992) · Zbl 0759.62015
[17] Hahn, J., Bootstrapping quantile regression models, Econometric Theory, 11, 105-121, (1995) · Zbl 1401.62045
[18] He, X.; Hu, F., Markov chain marginal bootstrap, Journal of the American Statistical Association, 97, 783-795, (2002) · Zbl 1048.62032
[19] Heckman, J. J.; Polachek, S., Empirical evidence on functional form of the earnings-schooling relationship, Journal of the American Statistical Association, 69, 350-354, (1974)
[20] Horowitz, J. L., Bootstrap methods for Median regression models, Econometrica, 66, 1327-1351, (1998) · Zbl 1056.62517
[21] Horowitz, J. L.; Lee, S., Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative, Journal of Econometrics, 152, 141-152, (2009) · Zbl 1431.62629
[22] Horowitz, J. L.; Spokoiny, V. G., An adaptive, rate-optimal test of linearity for Median regression models, Journal of the American Statistical Association, 97, 822-835, (2002) · Zbl 1048.62050
[23] Koenker, R., Quantile regression, (2005), Cambridge University Press New York · Zbl 1111.62037
[24] Koenker, R.; Bassett, G., Regression quantiles, Econometrica, 46, 33-50, (1978) · Zbl 0373.62038
[25] Koenker, R.; Hallock, K. F., Quantile regression, Journal of Economic Perspectives, 15, 4, 143-156, (2001)
[26] Koenker, R.; Machado, J. A.F., Goodness of fit and related inference processes for quantile regression, Journal of the American Statistical Association, 94, 1296-1310, (1999) · Zbl 0998.62041
[27] Mammen, E., Bootstrap and wild bootstrap for high-dimensional linear model, Annals of Statistics, 21, 225-285, (1993) · Zbl 0771.62032
[28] Mincer, J., Schooling, experience and earnings, (1974), Columbia University Press New York
[29] Murphy, K. M.; Welch, F., Empirical age-earnings profiles, Journal of Labor Economics, 8, 202-229, (1990)
[30] Neyman, J., Optimal asymptotic tests of composite statistical hypotheses, (Grenander, U., Probability and Statistics: The Harald Cramér Volume, (1959), Almqvist and Wiksell Stockholm), 213-234
[31] Otsu, T., 2009. RESET for quantile regression. Test 18, 381-391. · Zbl 1203.62086
[32] Ramsey, J. B., Tests for specification errors in classical linear least squares regression analysis, Journal of the Royal Statistical Society, Series B, 31, 350-371, (1969) · Zbl 0179.48902
[33] Rosenblatt, M., Conditional probability density and regression estimate, (Krishnaiah, P. R., Multivariate Analysis, II, (1969), Academic Press New York), 25-31
[34] Rothe, C.; Wied, D., Misspecification testing in a class of conditional distributional models, Journal of the American Statistical Association, 108, 314-324, (2013) · Zbl 06158345
[35] Sakov, A.; Bickel, P. J., An Edgeworth expansion for the \(m\) out of \(n\) bootstrapped Median, Statistics and Probability Letters, 49, 217-223, (2000) · Zbl 0969.62014
[36] van der Vaart, A. W., Asymptotic statistics, (1998), Cambridge University Press Cambridge, UK · Zbl 0910.62001
[37] van der Vaart, A. W.; Wellner, J. A., Weak convergence and empirical processes: with applications to statistics, (1996), Springer-Verlag, New York NY · Zbl 0862.60002
[38] Whang, Y.-J., Consistent specification testing for quantile regression models, (Corbae, D.; Durlauf, S. N.; Hansen, B. E., Econometric Theory and Practice: Frontiers of Analysis and Applied Research, (2006), Cambridge University Press New York), 288-308
[39] Whang, Y.-J., Smoothed empirical likelihood methods for quantile regression models, Econometric Theory, 22, 173-205, (2006) · Zbl 1138.62017
[40] Zheng, J. X., A consistent nonparametric test of parametric regression models under conditional quantile restrictions, Econometric Theory, 14, 123-138, (1998)
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