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Wild bootstrap for quantile regression. (English) Zbl 1228.62053
Summary: The existing theory of the wild bootstrap has focused on linear estimators. We broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators. As most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression, we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression. A simulation study on median regression is carried out to compare various bootstrap methods. With a simple finite-sample correction, the wild bootstrap is shown to account for general forms of heteroscedasticity in a regression model with fixed design points.

MSC:
62G09 Nonparametric statistical resampling methods
62G08 Nonparametric regression and quantile regression
65C60 Computational problems in statistics (MSC2010)
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