The Behavior of Robust Estimators on Dependent Data

Résumé du livre

The report studies the effect of serial dependence on the efficiency of various robust estimators of the location parameter. In order to show that the asymptotic distribution of these estimators is a normal distribution a slightly stronger mixing condition than Rosenblatt's strong mixing is introduced and it is shown that the empiric c.d.f. formed from such a process approaches a Gaussian process. In particular, first order autoregressive processes with Gaussian, Cauchy and double-exponential marginal distributions are shown to obey the conditions. The behavior of robust estimators on Gaussian processes is studied in greater detail. One general result states that for any Gaussian process with serial correlation (rho sub k)> 0 and summation (rho sub k)