Random rates in anisotropic regression

• 成果类型: Article
• 署名作者: Hoffmann, M; Lepski, O
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1021379858
• 发表日期: 2002
• 页码: 325-358
• 关键词: minimax adaptive estimation; asymptotic equivalence; confidence-intervals; spatial adaptation; wavelet; optimality; kernel; bounds

摘要

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.