A two sample test in high dimensional data

作者：Srivastava, Muni S.; Katayama, Shota^*; Kano, Yutaka

来源：Journal of Multivariate Analysis, 2013, 114: 349-358.

DOI：10.1016/j.jmva.2012.08.014

• High-dimensional data
• Hypothesis testing
• Behrens-Fisher problem
• Asymptotic theory

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.

• 出版日期2013-2