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A lack-of-fit test for quantile regression models with high-dimensional covariates. (English) Zbl 06921450
Summary: A new lack-of-fit test for quantile regression models, that is suitable even with high-dimensional covariates, is proposed. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates. To approximate the critical values of the test, a wild bootstrap mechanism convenient for quantile regression is used. An extensive simulation study was undertaken that shows the good performance of the new test, particularly when the dimension of the covariate is high. The test can also be applied and performs well under heteroscedastic regression models. The test is illustrated with real data about the economic growth of 161 countries.

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[1] Barro, R.J., Lee, J.W., 1994. Data set for a panel of 138 countries, discussion paper, NBER. http://www.nber.org/pub/barro.lee.
[2] Barro, R. J.; Sala-i-Martin, X., Economic growth, (1995), McGraw-Hill New York
[3] Escanciano, J. C., A consistent diagnostic test for regression models using projections, Econometric Theory, 22, 1030-1051, (2006) · Zbl 1170.62318
[4] Escanciano, J. C.; Goh, S. C., Specification analysis of linear quantile models, J. Econometrics, 178, 495-507, (2014) · Zbl 1293.62097
[5] Escanciano, J. C.; Velasco, C., Specification tests of parametric dynamic conditional quantiles, J. Econometrics, 159, 209-221, (2010) · Zbl 1431.62186
[6] Feng, X.; He, X.; Hu, J., Wild bootstrap for quantile regression, Biometrika, 98, 995-999, (2011) · Zbl 1228.62053
[7] García-Portugués, E.; González-Manteiga, W.; Febrero-Bande, M., A goodness-of-fit test for the functional linear model with scalar response, J. Comput. Graph. Statist., 23, 761-778, (2013)
[8] He, X.; Zhu, L.-X., A lack-of-fit test for quantile regression, J. Amer. Statist. Assoc., 98, 1013-1022, (2003) · Zbl 1043.62039
[9] Horowitz, J. L.; Spokoiny, V. G., An adaptive, rate-optimal test of linearity for Median regression models, J. Amer. Statist. Assoc., 97, 822-835, (2002) · Zbl 1048.62050
[10] Hurvich, C. M.; Tsai, C. L., Model selection for least absolute deviations regression in small samples, Statist. Probab. Lett., 9, 259-265, (1990)
[11] Koenker, R., Quantile regression, (2005), Cambridge University Press Cambridge · Zbl 1111.62037
[12] Koenker, R.; Bassett, G., Regression quantiles, Econometrica, 46, 33-50, (1978) · Zbl 0373.62038
[13] Koenker, R.; Machado, J. A.F., Goodness of fit and related inference processes for quantile regression, J. Amer. Statist. Assoc., 94, 1296-1310, (1999) · Zbl 0998.62041
[14] Lavergne, P.; Patilea, V., Breaking the curse of dimensionality in nonparametric testing, J. Econometrics, 143, 103-122, (2008) · Zbl 1418.62199
[15] Mammen, E., Bootstrap and wild bootstrap for high dimensional linear models, Ann. Statist., 21, 255-285, (1993) · Zbl 0771.62032
[16] Noh, H.; El Gouch, A.; Van Keilegom, I., Assessing model adequacy in possibly misspecified quantile regression, Comput. Statist. Data Anal., 57, 558-569, (2013) · Zbl 1365.62143
[17] Otsu, T., Conditional empirical likelihood estimation and inference for quantile regression models, J. Econometrics, 142, 508-538, (2008) · Zbl 1418.62165
[18] Stute, W., Nonparametric model checks for regression, Ann. Statist., 25, 613-641, (1997) · Zbl 0926.62035
[19] Stute, W.; Xu, W. L.; Zhu, L. X., Model diagnosis for parametric regression in high-dimensional spaces, Biometrika, 95, 451-467, (2008) · Zbl 1437.62614
[20] Whang, Y.-J., Smoothed empirical likelihood methods for quantile regression models, Econometric Theory, 22, 173-205, (2006) · Zbl 1138.62017
[21] Wilcox, R. R., Quantile regression: a simplified approach to a goodness-of-fit test, J. Data Sci., 6, 547-556, (2008)
[22] Zheng, J. X., A consistent test of functional form via nonparametric estimation techniques, J. Econometrics, 75, 263-289, (1996) · Zbl 0865.62030
[23] 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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