On high dimensional two-sample tests based on nearest neighbors

JOURNAL OF MULTIVARIATE ANALYSIS

卷:141

Article

Mondal, Pronoy K.¹  Biswas, Munmun¹  Ghosh, Anil K.¹ 

[1] Indian Stat Inst, Theoret Stat & Math Unit, Kolkata 700108, India

关键词: Central limit theorem;    HDLSS data;    Large sample test;    Law of large numbers;    Level and power of a test;    Permutation test;   

DOI  :  10.1016/j.jmva.2015.07.002

来源: Elsevier

【 摘 要 】

In this article, we propose new multivariate two-sample tests based on nearest neighbor type coincidences. While several existing tests for the multivariate two-sample problem perform poorly for high dimensional data, and many of them are not applicable when the dimension exceeds the sample size, these proposed tests can be conveniently used in the high dimension low sample size (HDLSS) situations. Unlike Schilling (1986) [26] and Henze's (1988) test based on nearest neighbors, under fairly general conditions, these new tests are found to be consistent in HDLSS asymptotic regime, where the sample size remains fixed and the dimension grows to infinity. Several high dimensional simulated and real data sets are analyzed to compare their empirical performance with some popular two-sample tests available in the literature. We further investigate the behavior of these proposed tests in classical asymptotic regime, where the dimension of the data remains fixed and the sample size tends to infinity. In such cases, they turn out to be asymptotically distribution-free and consistent under general alternatives. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free