Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)
The Annals of Statistics · 2002 · Volume 30 · Issue 2
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.
Keywords
62G07, 62G10, 62G15, anisotropic regression, minimax theory, nonparametric estimation, random normalizing factors
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