Measures of the Sensitivity of Regression Estimates to the Choice of Estimator

Abstract

Let Y 1 , …, Y n denote independent real-valued observations, each of the form Y j = X j β + σε j , where X j is a fixed covariate vector, β and σ are unknown parameters ε 1 , …, ε n are identically distributed according to a symmetric density p . This article considers the sensitivity of point estimates of β to the choice of estimator from classes of estimators based on the L estimators of Kroenker and Portnoy. Specific measures of sensitivity are proposed these measures are applied to several datasets.