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 ε₁, …, 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.

Key Words:

• Conditional inference
• Regression models
• Regression quantiles
• Robust estimation