Asymptotic normality of the least sum of squares of trimmed residuals estimator

TL;DR

This paper establishes the asymptotic normality of the least sum of squares of trimmed residuals estimator, a robust alternative to the classic least squares estimator, enhancing understanding of its statistical properties.

Contribution

It provides the first proof of the asymptotic normality of the LST estimator, filling a key gap in its theoretical foundation.

Findings

Proves asymptotic normality of the LST estimator

Confirms strong and root-n consistency of LST

Enhances the theoretical understanding of robust estimators

Abstract

To enhance the robustness of the classic least sum of squares (LS) of the residuals estimator, Zuo (2022) introduced the least sum of squares of trimmed (LST) residuals estimator. The LST enjoys many desired properties and serves well as a robust alternative to the LS. Its asymptotic properties, including strong and root-n consistency, have been established whereas the asymptotic normality is left unaddressed. This article solves this remained problem.