Variance estimation for high-dimensional regression models

Vladimir G. Spokoiny

No 1999,86, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

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-4jd which is worse than n-1/2 . The rate optimal estimating procedure is presented.

Date: 1999
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