Brown-Mood Type Median Estimators for Simple Regression Models

Abstract

In the context of simple linear regression we investigate a class of estimators for the parameters which contains the Brown-Mood estimators. We derive the asymptotic efficiency properties of the class of slope estimators and find the most efficient slope estimator. This estimator is shown to have efficiency properties analogous to those of other median estimators for slope found in the literature. The equations which define the optimal estimators are median analogues of the least squares normal equation.