Behavior of Robust Estimators in the Regression Model with Dependent Errors

Abstract

This paper proves the asymptotic linearity in the regression parameter of a class of linear rank statistics when errors in the regression model are strictly stationary and strongly mixing. Besides this, several other weak convergence results are proved which yield the asymptotic normality of $L$ and $M$ estimators of the regression parameter under the above dependent structure. All these results are useful in studying the effect of the above dependence on the asymptotic behavior of $R, M$ and $L$ estimators vis-a-vis the least squares estimator. An example of linear model with Gaussian errors is given where it is shown that the asymptotic efficiency of certain classes of $R, M$ and $L$ estimators relative to the least squared estimator is greater than or equal to its value under the usual independent errors model.