Wild residual bootstrap inference for penalized quantile regression with heteroscedastic errors
(2018) Biometrika — Vol. 105, n° 4, p. 859-872 (2018)
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- We consider a heteroscedastic regression model in which some of the regression coefficients are zero but it is not known which ones. Penalized quantile regression is a useful approach for analysing such data. By allowing different covariates to be relevant for modelling conditional quantile functions at different quantile levels, it provides a more complete picture of the conditional distribution of a response variable than mean regression. Existing work on penalized quantile regression has been mostly focused on point estimation.Although bootstrap procedures haverecentlybeenshowntobeeffectiveforinferenceforpenalizedmeanregression,theyarenot directly applicable to penalized quantile regression with heteroscedastic errors. We prove that a wild residual bootstrap procedure for unpenalized quantile regression is asymptotically valid for approximating the distribution of a penalized quantile regression estimator with an adaptive L1 penaltyandthatamodifiedversioncanbeusedtoapproximatethedistributionofaL1-penalized quantile regression estimator. The new methods do not require estimation of the unknown error densityfunction.Weestablishconsistency,demonstratefinite-sampleperformance,andillustrate the applications on a real data example
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Wang, L., Van Keilegom, I., & Maidman, A. (2018). Wild residual bootstrap inference for penalized quantile regression with heteroscedastic errors. Biometrika, 105(4), 859-872. https://doi.org/10.1093/biomet/asy037 (Original work published 2018)