TESTS ALTERNATIVE TO HIGHER CRITICISM FOR HIGH-DIMENSIONAL MEANS UNDER SPARSITY AND COLUMN-WISE DEPENDENCE

被引：44

作者：

Zhong, Ping-Shou ^{[1
]}

Chen, Song Xi ^{[2
,3
,4
]}

Xu, Minya ^{[2
,3
]}

机构：

[1] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

[2] Peking Univ, Guanghua Sch Management, Dept Business Stat & Econometr, Beijing 100871, Peoples R China

[3] Peking Univ, Ctr Stat Sci, Beijing 100871, Peoples R China

[4] Iowa State Univ, Dept Stat, Ames, IA 50011 USA

来源：

ANNALS OF STATISTICS | 2013年 / 41卷 / 06期

基金：

美国国家科学基金会;

关键词：

Large deviation; large p; small n; optimal detection boundary; sparse signal; thresholding; weak dependence; CENTRAL LIMIT-THEOREMS; MIXTURES;

D O I：

10.1214/13-AOS1168

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 consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding L-1 and L-2 statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal strength and sparsity. The two alternative tests can attain the same detection boundary of the Higher Criticism test in [Ann. Statist. 32 (2004) 962-994] which was established for uncorrelated Gaussian data. It is demonstrated that the maximal L-2-thresholding test is at least as powerful as the maximal L-1-thresholding test, and both the maximal L-2 and L-1-thresholding tests are at least as powerful as the Higher Criticism test.

引用

页码：2820 / 2851

页数：32