Two Sample Test For High Dimensional Data

Two sample test for high dimensional data analysis mentioned in my thesis is to test the means for data sets with dimensionality p, which goes to infinity. This is of great interest recently motivated by real applied statistical analysis, and also becomes manageable since modern computational techniques improve dramatically. A two sample test statistic for means of high dimensional data is proposed by Bai and Saranadasa (1996).However, the BS test statistic only deals with the overall test. If the null hypothesis is rejected, no further information is available for the individual components of the null hypothesis. This is a fatal problem in micro-array analysis, which is interested in the so called multiple comparison, a multiple test procedure on all of the individual components of the null hypotheses.Two famous multiple comparison procedures are introduced by Bonferroni which is based on the control of the family-wise error rate (FWER) and by Benjamini and Hochberg (1995) which is based on the control of the false discovery rate (FDR).The purpose of this thesis is to compare the performance of these three test procedures. I will present the simulation results in details given the same data generating mechanism. The main idea is to see how the power looks when p increases and so does the sample size.