Bias-reduced estimation of mean absolute deviation around the median

TL;DR

This paper introduces a bias-reduced estimator for the mean absolute deviation around the median in regression models, addressing smoothness issues and demonstrating effectiveness through theoretical properties and simulations.

Contribution

It presents a novel bias correction method for median regression's mean absolute deviation, overcoming smoothness limitations and applicable in high-dimensional contexts.

Findings

The estimator effectively reduces bias in median regression.

Theoretical properties like local asymptotic normality are established.

Simulation results indicate good performance in high-dimensional settings.

Abstract

A bias-reduced estimator is proposed for the mean absolute deviation parameter of a median regression model. A workaround is devised for the lack of smoothness in the sense conventionally required in general bias-reduced estimation. A local asymptotic normality property and a Bahadur--Kiefer representation suffice in proving the validity of the bias correction. The proposal is developed under a classical asymptotic regime but, based on simulations, it seems to work also in high-dimensional settings.