On high dimensional two sample mean testing statistics: a comparative study with a data adaptive choice of coefficient vector
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.
Comput. Stat.