Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean

TL;DR

This paper develops Bahadur representations for the bootstrap median absolute deviation and applies these results to analyze the bootstrap sample projection depth weighted mean, a robust location estimator.

Contribution

It provides new strong and weak Bahadur representations for bootstrap MAD and extends these results to the bootstrap projection depth weighted mean.

Findings

Derived strong and weak Bahadur representations for bootstrap MAD.

Established weak Bahadur representation for bootstrap projection depth weighted mean.

Enhanced understanding of the asymptotic properties of robust estimators.

Abstract

Median absolute deviation (hereafter MAD) is known as a robust alternative to the ordinary variance. It has been widely utilized to induce robust statistical inferential procedures. In this paper, we investigate the strong and weak Bahadur representations of its bootstrap counterpart. As a useful application, we utilize the results to derive the weak Bahadur representation of the bootstrap sample projection depth weighted mean---a quite important location estimator depending on MAD.