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On high-dimensional two sample mean testing statistics: a comparative study with a data adaptive choice of coefficient vector
- On high-dimensional two sample mean testing statistics: a comparative study with a data adaptive choice of coefficient vector
- Kim, Soeun; Ahn, Jae Youn; Lee, Woojoo
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- COMPUTATIONAL STATISTICS
- 0943-4062; 1613-9658
- vol. 31, no. 2, pp. 451 - 464
- High dimension; Two sample mean test; Coefficient vector; Data adaptive
- SPRINGER HEIDELBERG
- SCIE; SCOPUS
- The key issues involved in two sample tests in high dimensional problems arise due to large dimension of the mean vector for a relatively small sample size. Recently, Wang et al. (Stat Sin 23:667-690, 2013) proposed a jackknife empirical likelihood test that works under weak assumptions on the dimension of variables (p), and showed that the test statistic has a chi-square limit regardless of whether p is finite or diverges. The sufficient condition required for this statistic is still restrictive. In this paper we significantly relax the sufficient condition for the asymptotic chi-square limit with models allowing flexible dependence structures and derive simpler alternative statistics for testing the equality of two high dimensional means. The proposed statistics have a chi-squared distribution or the maximum of two independent chi-square statistics as their limiting distributions, and the asymptotic results hold for either finite or divergent p. We also propose a data-adaptive method to select the coefficient vector, and compare the various methods in simulation studies. The proposed choice of coefficient vector substantially increases power in the simulation.
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