TY - JOUR
T1 - A two sample test in high dimensional data
AU - Srivastava, Muni S.
AU - Katayama, Shota
AU - Kano, Yutaka
N1 - Funding Information:
We would like to thank the associate editor and two referees for their careful reading of the original article and for their valuable suggestions that greatly helped improve the presentation. The research of Srivastava was supported by the Natural Sciences and Engineering Research Council of Canada , Katayama was supported by the Grant-in-Aid for JSPS Fellows and Kano was supported by the Grant-in-Aid for Challenging Exploratory Research and Grant-in-Aid for Scientific Research (B) .
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Asymptotic theory
KW - Behrens-Fisher problem
KW - High-dimensional data
KW - Hypothesis testing
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U2 - 10.1016/j.jmva.2012.08.014
DO - 10.1016/j.jmva.2012.08.014
M3 - Article
AN - SCOPUS:84867812899
SN - 0047-259X
VL - 114
SP - 349
EP - 358
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 1
ER -