Testing of Location Parameters Against Restricted Alternatives with Optimal Choice of Weights

Testing of equality of populations is one of the fundamental problems in Science. In this paper, we propose a new class of nonparametric tests for testing of location parameters of the distribution of populations against restricted alternatives. The asymptotic distribution of the proposed test statistics is derived. In order to attain maximum efficiency of the proposed tests, a general optimal choice of weights of the proposed class of test statistics is established. Pitman asymptotic relative efficiency and simulation study is carried out of the proposed class of tests. An illustrative example is provided to see the execution of the proposed test.