Empirical process of residuals for high-dimensional linear models

• 成果类型: Article
• 署名作者: Mammen, E
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 307-335
• 关键词: p-regression parameters; asymptotic-behavior; robust regression; M-ESTIMATORS; bootstrap; p2/n

摘要

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