Median bias of M-estimators

TL;DR

This paper derives bounds on the median bias of univariate M-estimators under mild conditions and discusses median bias in some multivariate cases, highlighting limitations in convergence implications.

Contribution

It provides new bounds on median bias for univariate M-estimators and explores median bias in multivariate cases, expanding understanding of estimator bias properties.

Findings

Bounds on median bias for univariate M-estimators

Median bias analysis for some multivariate M-estimators

Regularity conditions do not ensure convergence in distribution

Abstract

In this note, we derive bounds on the median bias of univariate M-estimators under mild regularity conditions. These requirements are not sufficient to imply convergence in distribution of the M-estimators. We also discuss median bias of some multivariate M-estimators.