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February 1996 Empirical process of residuals for high-dimensional linear models
Enno Mammen
Ann. Statist. 24(1): 307-335 (February 1996). DOI: 10.1214/aos/1033066211


We give a stochastic expansion for the empirical distribution function $\hat{F}_n$ of residuals in a p-dimensional linear model. This expansion holds for p increasing with n. It shows that, for high-dimensional linear models, $\hat{F}_n$ strongly depends on the chosen estimator $\hat{\theta}$ of the parameter $\theta$ of the linear model. In particular, if one uses an ML-estimator $\hat{\theta}_{ML}$ which is ML motivated by a wrongly specified error distribution function G, then $\hat{F}_n$ 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.


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Enno Mammen. "Empirical process of residuals for high-dimensional linear models." Ann. Statist. 24 (1) 307 - 335, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62042
MathSciNet: MR1389892
Digital Object Identifier: 10.1214/aos/1033066211

Primary: 62G30
Secondary: 62J05 , 62J20

Keywords: asymptotics with increasing dimension , Empirical processes , linear models , residuals

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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