Linear Ordered Rank Tests Which are Asymptotically Efficient for the Two-Sample Problem
Jayant V. Deshpandé · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1972
Summary In this paper the nonparametric two-sample problem is considered and tests are proposed for the hypothesis of identity of the two distribution functions. These tests are based on statistics which are linear combinations of ranks of the order statistics of one of the samples, in the two-sample rank order. It is seen that many existing statistics, proposed mainly on heuristic grounds, are members of this class. The asymptotic distribution of such statistics is discussed and those statistics which lead to tests with maximum ARE in this class are derived. It is seen that their ARE with respect to the “optimal” parametric tests is 1. In the appendix, we give the coefficients to be used for forming linear combinations which lead to the maximum ARE in certain specific cases. The work reported here was carried out when the author was a Visiting Fellow at the University of Sheffield.