Asymptotic normality of whitened $M$-estimates

Whitened $M$-estimates are considered that have been introduced in 1 for the parameters of a linear model with errors of the moving average type. Asymptotic normality of whitened $M$-estimates is proved under general assumptions on the distribution of errors and on of the model entry vectors. As a corrollary, an improvement of some earlier results on asymptotic normality of Huber's $M$-estimates of regression is obtained. The asymptotic efficiency and robustness of whitened $M$-estimates is discussed. $M$-estimates are shown to be less efficient than whitened $M$-estimates in the presence of dependent errors of the moving average type.