Bias correction for quantile regression estimators

Abstract

We study the bias of classical quantile regression and instrumental variable quantile regression estimators. While being asymptotically first-order unbiased, these estimators can have non-negligible second-order biases. We derive a higher-order stochastic expansion of these estimators using empirical process theory. Based on this expansion, we derive an explicit formula for the second-order bias and propose a feasible bias correction procedure that uses finite-difference estimators of the bias components. The proposed bias correction method performs well in simulations. We provide an empirical illustration using Engel's classical data on household food expenditure.

References in corpus (5)

• Extremal quantile regression
• Gaussian approximation of suprema of empirical processes
• Smoothed estimating equations for instrumental variables quantile regression
• Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks
• Nearly root-n approximation for regression quantile processes