Empirical process of residuals for high-dimensional linear models

• Verfasst von: Mammen, Enno [VerfasserIn]
• Titel: Empirical process of residuals for high-dimensional linear models
• Verf.angabe: Enno Mammen
• Fussnoten: First available in Project Euclid: 26 September 2002 ; Gesehen am 22.02.2018
• Titel Quelle: Enthalten in: The annals of statistics
• Jahr Quelle: 1996
• Band/Heft Quelle: 24(1996), 1, S. 307-335$19
• ISSN Quelle: 2168-8966
• DOI: doi:10.1214/aos/1033066211
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1570095302

Abstract

We give a stochastic expansion for the empirical distribution function F^nF^n\hat{F}_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^nF^n\hat{F}_n strongly depends on the chosen estimator θ^θ^\hat{\theta} of the parameter θθ\theta of the linear model. In particular, if one uses an ML-estimator θ^MLθ^ML\hat{\theta}_{ML} which is ML motivated by a wrongly specified error distribution function G, then F^nF^n\hat{F}_n is biased toward G. For p^2 / n \to \infty$, 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.