Empirical process of residuals for high-dimensional linear models
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{\the...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1996
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| In: |
The annals of statistics
Year: 1996, Volume: 24, Issue: 1, Pages: 307-335$19 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1033066211 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1033066211 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1033066211 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1033066211 
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| Author Notes: | Enno Mammen |
| Summary: | We give a stochastic expansion for the empirical distribution function F^nF^n\hat{F}_n of residuals in a p-dimensional linear model. This expansion holds for p increasing with n. It shows that, for high-dimensional linear models, F^nF^n\hat{F}_n strongly depends on the chosen estimator θ^θ^\hat{\theta} of the parameter θθ\theta of the linear model. In particular, if one uses an ML-estimator θ^MLθ^ML\hat{\theta}_{ML} which is ML motivated by a wrongly specified error distribution function G, then F^nF^n\hat{F}_n is biased toward G. For p^2 / n \to \infty$, 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. |
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| Item Description: | First available in Project Euclid: 26 September 2002 Gesehen am 22.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1033066211 |