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April 2002 Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)
M. Hoffman, O. Lepski
Ann. Statist. 30(2): 325-396 (April 2002). DOI: 10.1214/aos/1021379858

Abstract

In the context of minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of selecting significant variables in Gaussian white noise. In particular, we show that our method essentially improves the accuracy of estimation, in the sense of giving explicit improved confidence sets in $L_2$-norm. Links to adaptive estimation are discussed.

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M. Hoffman. O. Lepski. "Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)." Ann. Statist. 30 (2) 325 - 396, April 2002. https://doi.org/10.1214/aos/1021379858

Information

Published: April 2002
First available in Project Euclid: 14 May 2002

MathSciNet: MR1902892
Digital Object Identifier: 10.1214/aos/1021379858

Subjects:
Primary: 62G07, 62G10, 62G15

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 2 • April 2002
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