A Note on Location Parameter Estimation using the Weighted Hodges-Lehmann Estimator

TL;DR

This paper introduces two new weighted Hodges-Lehmann estimators designed to improve location parameter estimation in contaminated data scenarios, demonstrating superior robustness and efficiency through extensive simulations.

Contribution

It proposes novel weighted Hodges-Lehmann estimators that incorporate weight factors, enhancing robustness over traditional estimators in contaminated data environments.

Findings

Proposed WHL estimators outperform traditional methods in robustness.

WHL estimators show higher breakdown points and lower bias.

Simulations confirm improved efficiency of WHL estimators.

Abstract

Robust design is one of the main tools employed by engineers for the facilitation of the design of high-quality processes. However, most real-world processes invariably contend with external uncontrollable factors, often denoted as outliers or contaminated data, which exert a substantial distorting effect upon the computed sample mean. In pursuit of mitigating the inherent bias entailed by outliers within the dataset, the concept of weight adjustment emerges as a prudent recourse, to make the sample more representative of the statistical population. In this sense, the intricate challenge lies in the judicious application of these diverse weights toward the estimation of an alternative to the robust location estimator. Different from the previous studies, this study proposes two categories of new weighted Hodges-Lehmann (WHL) estimators that incorporate weight factors in the location parameter estimation. To evaluate their robust performances in estimating the location parameter, this study constructs a set of comprehensive simulations to compare various location estimators including mean, weighted mean, weighted median, Hodges-Lehmann estimator, and the proposed WHL estimators. The findings unequivocally manifest that the proposed WHL estimators clearly outperform the traditional methods in terms of their breakdown points, biases, and relative efficiencies.