ON COMBINATORIAL TESTING PROBLEMS

被引：70

作者：

Addario-Berry, Louigi ^{[1
]}

Broutin, Nicolas ^{[2
]}

Devroye, Luc ^{[3
]}

Lugosi, Gabor ^{[4
,5
]}

机构：

[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

[2] INRIA Rocquencourt, F-78153 Le Chesnay, France

[3] McGill Univ, Sch Comp Sci, Montreal, PQ H3A 2A7, Canada

[4] ICREA, Barcelona, Spain

[5] Pompeu Fabra Univ, Dept Econ, Barcelona, Spain

来源：

ANNALS OF STATISTICS | 2010年 / 38卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Hypothesis testing; multiple hypotheses; Gaussian processes; HIGH DIMENSION; UNIFORM;

D O I：

10.1214/10-AOS817

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study a class of hypothesis testing problems in which, upon observing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been "contaminated," that is, have a mean different from zero. We establish some general conditions under which testing is possible and others under which testing is hopeless with a small risk. The combinatorial and geometric structure of the class of sets is shown to play a crucial role. The bounds are illustrated on various examples.

引用

页码：3063 / 3092

页数：30

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