ABSTRACT
In Chapter 1 the concept of Pittman efficiency was defined as a criterion for the comparison of any two test statistics. Many of the non-parametric tests covered in this book can be considered direct analogs of some classical test which is known to be most powerful under certain specific distribution assumptions. The asymptotic efficiencies of the nonparametric tests relative to a “best” test have been simply stated here without discussion. In this chapter we shall investigate the concept of efficiency more thoroughly and prove some theorems which simplify the calculation. The theory will then be illustrated by applying it to various tests covered in earlier chapters in order to derive numerical values of the ARE for some particular distributions. The theory presented here is generally attributed to Pitman; Noether (1955) gives important generalizations of the theory.
