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