Wild bootstrap for quantile regression

TLDR

Existing wild bootstrap theory focuses on linear estimators, but most weight distributions bias variance estimates for nonlinear linear regression, motivating a broader class for quantile regression. The study aims to broaden wild bootstrap validity by providing a class of weight distributions asymptotically valid for quantile regression estimators. The authors modify the wild bootstrap to accept a broader class of weight distributions for quantile regression and evaluate it via a simulation study on median regression comparing various bootstrap methods. A simple finite‑sample correction enables the wild bootstrap to account for general heteroscedasticity in fixed‑design regression models.

Abstract

The existing theory of the wild bootstrap has focused on linear estimators. In this note, 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.