WIAS Preprint No. 503, (1999)

Variance estimation for high-dimensional regression models



Authors

  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62G20

Keywords

  • variance estimation, regression, high dimension

Abstract

The paper is concerned with the problem of variance estimation for a high-dimensional 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 higher dimensional model, the optimal accuracy is n-4/d which is worse than n-1/2. The rate optimal estimating procedure is presented.

Appeared in

  • Journal of Multivariate Analysis, 82(2002), pp. 111-133

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