Risk hull method and regularization by projections of ill-posed inverse problems
成果类型：
Article
署名作者：
Cavalier, L.; Golubev, Yu.
署名单位：
Aix-Marseille Universite
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053606000000542
发表日期：
2006
页码：
1653-1677
关键词：
摘要：
We study a standard method of regularization by projections of the linear inverse problem Y = Af + epsilon, where epsilon is a white Gaussian noise, and A is a known compact operator with singular values converging to zero with polynomial decay. The unknown function f is recovered by a projection method using the singular value decomposition of A. The bandwidth choice of this projection regularization is governed by a data-driven procedure which is based on the principle of risk hull minimization. We provide nonasymptotic upper bounds for the mean square risk of this method and we show, in particular, that in numerical simulations this approach may substantially improve the classical method of unbiased risk estimation.