JOURNAL OF MULTIVARIATE ANALYSIS | 卷:114 |
A two sample test in high dimensional data | |
Article | |
Srivastava, Muni S.2  Katayama, Shota1  Kano, Yutaka1  | |
[1] Osaka Univ, Grad Sch Engn Sci, Toyonaka, Osaka 5608531, Japan | |
[2] Univ Toronto, Dept Stat, Toronto, ON M5S 3G3, Canada | |
关键词: High-dimensional data; Hypothesis testing; Behrens-Fisher problem; Asymptotic theory; | |
DOI : 10.1016/j.jmva.2012.08.014 | |
来源: Elsevier | |
【 摘 要 】
In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N-1 and N-2 independently distributed p-dimensional observation vectors. It will be assumed that N-1 observation vectors from the first group are normally distributed with mean vector mu(1) and covariance matrix Sigma(1). Similarly, the N-2 observation vectors from the second group are normally distributed with mean vector mu(2) and covariance matrix Sigma(2). We propose a test for testing the hypothesis that mu(1) = mu(2). This test is invariant under the group of p x p nonsingular diagonal matrices. The asymptotic distribution is obtained as (N-1, N-2, p) -> infinity and N-1/(N-1 + N-2) -> k is an element of (0, 1) but N-1/p and N-2/p may go to zero or infinity. It is compared with a recently proposed non-invariant test. It is shown that the proposed test performs the best. (C) 2012 Elsevier Inc. All rights reserved.
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