Adaptive prediction and estimation in linear regression with infinitely many parameters
成果类型：
Article
署名作者：
Goldenshluger, A; Tsybakov, A
署名单位：
University of Haifa; Sorbonne Universite
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
2001
页码：
1601-1619
关键词：
摘要：
The problem of adaptive prediction and estimation in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that is sharp asymptotically minimax adaptive over ellipsoids in l(2). The method consists in an application of blockwise Stein's rule with weakly geometrically increasing blocks to the penalized least squares fits of the first N coefficients. To prove the results we develop oracle inequalities for a sequence model with correlated data.