SOME SIMPLE HIGH DIMENSIONAL ONE AND TWO SAMPLE TESTS

Abstract

Consider testing H0: mu= 0 versus HA : mu is not 0 using a random sample of size n where the xi are p ×1 random vectors and p may be much larger than n. Several one sample tests use the same test statistic Tn with different estimators of the variance V(Tn). Rather simple theory from U-statistics is used to find V(Tn), resulting in an estimator that is quick to compute when H0 is true. Some two sample tests for H0: mu1 = mu2 are also considered.