Weak Convergence of a Two-sample Empirical Process and a New Approach to Chernoff-Savage Theorems

Abstract

An empirical stochastic process for two-sample problems is defined and its weak convergence studied. The results are based upon an identity which relates the two-sample empirical process to the more usual one-sample empirical process. Based on this identity a relatively simple proof of a Chernoff-Savage theorem is obtained. The c-sample analogues of these results are also included.