Minimum Distance Estimation in a Linear Regression Model

Abstract

This paper discusses a class of minimum distance Cramer-Von Mises type estimators of the slope parameter in a linear regression model. These estimators are obtained by minimizing an integral of squared difference between weighted empiricals of the residuals and their expectations with respect to a large class of integrating measures. The estimator corresponding to the weights proportional to the design variable is shown to be asymptotically efficient within the class at a given error distribution. The paper also discusses the asymptotic null distribution of a class of minimum Cramer-Von Mises type goodness-of-fit test statistics.