文章基本信息

标题：Estimation and detection of functions from anisotropic Sobolev classes
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作者：Yuri Ingster ; Natalia Stepanova
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2011
卷号：5
页码：484-506
DOI：10.1214/11-EJS615
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problems of estimating and detecting an unknown function f depending on a multidimensional variable (for instance, an image) observed in the Gaussian white noise. It is assumed that f belongs to anisotropic Sobolev class. The case of a function of infinitely many variables is also considered. An asymptotic study (as the noise level tends to zero) of the estimation and detection problems is done. In connection with the estimation problem, we construct asymptotically minimax estimators and establish sharp asymptotics for the minimax integrated squared risk. In the detection problem, we construct asymptotically minimax tests and provide conditions for distinguishability in the problem.
关键词：Nonparametric estimation;nonparametric sig nal detection;Gaussian white noise;multivariate functions;anisotropic smoothness.