文章基本信息

标题：Non asymptotic minimax rates of testing in signal detection with heterogeneous variances
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作者：Béatrice Laurent ; Jean-Michel Loubes ; Clément Marteau 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2012
卷号：6
页码：91-122
DOI：10.1214/12-EJS667
语种：English
出版社：Institute of Mathematical Statistics
摘要：The aim of this paper is to establish non-asymptotic minimax rates for goodness-of-fit hypotheses testing in an heteroscedastic setting. More precisely, we deal with sequences (Yj)j∈J of independent Gaussian random variables, having mean (θj)j∈J and variance (σj)j∈J. The set J will be either finite or countable. In particular, such a model covers the inverse problem setting where few results in test theory have been obtained. The rates of testing are obtained with respect to l2 norm, without assumption on (σj)j∈J and on several functions spaces. Our point of view is entirely non-asymptotic.