On a Distribution-free Method of Estimating Asymptotic Efficiency of a Class of Non-parametric Tests

1. Summary. This paper deals with some aspects of nonparametric confidence intervals for shift and scale parameters which may be obtained from a celebrated class of rank order tests for the location and scale problems. This also provides a distribution-free method of estimating asymptotic efficiency of a class of tests and estimates (point as well as intervals) that may be derived from the same class of rank order statistics. Further, the proposed method is also applicable for estimating certain functionals of the distribution function which may not be otherwise estimated in a simple manner. 2. Introduction. Let X1, ..., Xm and Y1, ***, Yn be two independent random samples of sizes m and n, drawn from populations with absolutely continuous cumulative distribution functions (cdf) F(x) and G(x), respectively. For testing the null hypothesis of the identity of F and G, a class of non-parametric tests can be represented in terms of Chernoff-Savage [1] type of teststatistics of the form