A two sample test in high dimensional data

Muni S. Srivastava, Shota Katayama, Yutaka Kano

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N1 and N2 independently distributed p-dimensional observation vectors. It will be assumed that N1 observation vectors from the first group are normally distributed with mean vector μ1 and covariance matrix Σ1. Similarly, the N2 observation vectors from the second group are normally distributed with mean vectorμ2 and covariance matrixΣ2.Wepropose a test for testing the hypothesis that μ1 = μ2. This test is invariant under the group of p×p nonsingular diagonal matrices. The asymptotic distribution is obtained as (N1, N2, p) → ∞and N1/(N1 + N2) → k ∈ (0, 1) but N1/p and N2/p may go to zero or infinity. It is compared with a recently proposed noninvariant test. It is shown that the proposed test performs the best.

Original languageEnglish
Pages (from-to)349-358
Number of pages10
JournalJournal of Multivariate Analysis
Issue number1
Publication statusPublished - 2013
Externally publishedYes


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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