Testing Heteroscedasticity in Robust Regression

Abstract

This work studies the phenomenon of heteroscedasticity and its consequences for various robust estimation methods for the linear regression, including the least weighted squares, regression quantiles and trimmed least squares estimators. We investigate hypothesis tests for these regression methods and removing heteroscedasticity from the linear regression model. The new asymptotic heteroscedasticity tests for robust regression are asymptotically equivalent to standard tests computed for the least squares regression. Also we describe an asymptotic approximation to the exact null distribution of the test statistics. We describe a robust estimation procedure for the linear regression with heteroscedastic errors.