EMPIRICAL PROCESS OF RESIDUALS FOR HIGH-DIMENSIONAL LINEAR-MODELS

We give a stochastic expansion for the empirical distribution function (F) over cap(n)$ Of residuals in a p-dimensional linear model. This e xpansion holds for p increasing with n. It shows that, for high-dimens ional linear models, (F) over cap(n)$ strongly depends on the chosen e stimator <(theta)over cap> of the parameter theta of the linear model. In particular, if one uses an ML-estimator <(theta)over cap (ML)> whi ch is motivated by a wrongly specified error distribution function G, then (F) over cap(n)$ is biased toward G. For p(2)/n --> infinity, thi s bias effect is of larger order than the stochastic fluctuations of t he empirical process. Hence, the statistical analysis may just reprodu ce the assumptions imposed.