Functional aggregation for nonparametric regression

• 成果类型: Article
• 署名作者: Juditsky, A; Nemirovski, A
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Technion Israel Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 681-712
• 关键词: projection pursuit regression; approximation; bounds

摘要

We consider the problem of estimating an unknown function f from N noisy observations on a random grid. In this paper we address the following aggregation problem: given M functions f(1),...,f(M) find an aggregated estimator which approximates f nearly as well as the best convex combination f* of f(1),...,f(M). We propose algorithms which provide approximations of f* with expected L-2 accuracy O(N(-1/)4 ln(1/4) M). We show that this approximation rate cannot be significantly improved. We discuss two specific applications: nonparametric prediction for a dynamic system with output nonlinearity and reconstruction in the Jones-Barron class.