A GENERAL CLASSIFICATION RULE FOR PROBABILITY-MEASURES
成果类型：
Article
署名作者：
KULKARNI, SR; ZEITOUNI, O
署名单位：
Technion Israel Institute of Technology; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Lincoln Laboratory
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176324714
发表日期：
1995
页码：
1393-1407
关键词：
摘要：
We consider the composite hypothesis testing problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of all probability measures M(1)(Sigma) over some compact Polish space Sigma, we want to decide whether or not the unknown distribution belongs to A or its complement. We propose an algorithm which leads a.s. to a correct decision for any A satisfying certain structural assumptions. A refined decision procedure is also presented which, given a countable collection A(i) subset of M(1)(Sigma), i = 1, 2,..., each satisfying the structural assumption, will eventually determine a.s. the membership of the distribution in any finite number of the A(i). Applications to density estimation are discussed.
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