Robustness of T-Test

摘要

The standard optimum properties like UMP, UMPU, UMPS, UMPI, of the familiar Student's t-test for testing the significance of the mean of a univariate normal population with unknown variance against one-sided of both-sided alternatives are well-known. This paper shows mainly without invariance that the t-test continues to be optimum when normality is replaced by a class of elliptically symmetric distributions, thereby establishing optimality robustness of the t-test.