A Class of Nonparametric Tests for the Two-Sample Location Problem

The two-sample location problem is one of the fundamental problems encountered in Statistics. In many applications of Statistics, two-sample problems arise in such a way as to lead naturally to the formulations of the null hypothesis to the effect that the two samples come from identical populations. A class of nonparametric test statistics is proposed for two-sample location problem based on U-statistic with the kernel depending on a constant ’a’ when the underlying distribution is symmetric. The optimal choice of ’a’ for different underlying distributions is determined. An alternative expression for the class of test statistics is established. Pitman asymptotic relative efficiencies indicate that the proposed class of test statistics does well in comparison with many of the test statistics available in the literature. The small sample performance is also studied through Monte-Carlo Simulation technique