Durbin-Watson Statistic For The Least Trimmed Squares

The famous Durbin-Watson statistic is studied for the residuals from the least trimmed squared regression analysis. Having proved asymptotic linearity of corresponding functional (namely sum of h smallest squared residuals), an asymptotic representation of the least trimmed squares estimator is established. It is then used to modify D-W considerations which led to the analytically tractable form of D-W statistic. It appeared that in the modified D-W statistic for the least trimmed squares the terms which are different from the terms appearing in D-W statistic for the ordinary least squares, contain only a finite number of summands. Since all these terms are uniformly with respect to the number of observations bounded in probability, it is clear that asymptotically both versions, the first one for the ordinary least squares and the second for the least trimmed squares, are equivalent. Nevertheless some rough analysis of behaviour for finite samples is included at the end of paper.