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Variance Estimation for High-Dimensional Regression Models

✍ Scribed by Vladimir Spokoiny

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 190 KB
Volume: 82
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.2001.2023

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✦ Synopsis

The paper is concerned with the problem of variance estimation for a highdimensional regression model. The results show that the accuracy n -1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of the model. In particular, for a two times differentiable regression function, the rate n -1/2 is achievable only for dimensionality smaller or equal to 8. For a higher dimensional model, the optimal accuracy is n -4/d which is worse than n -1/2 . The rate optimal estimating procedure is presented.

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