Asymptotic Efficiency of Nonparametric Tests

A unified treatment that presents powerful new methods to evaluate explicitly different kinds of efficiencies.

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.

Introduction; 1. Asymptotic efficiency of statistical tests and mathematical means for its computation; 2. Asymptotic efficiency of nonparametric goodness-of-fit tests; 3. Asymptotic efficiency of nonparametric homogeneity tests; 4. Asymptotic efficiency of nonparametric symmetry tests; 5. Asymptotic efficiency of nonparametric independence tests; 6. Local asymptotic optimality of nonparametric tests and the characterisation of distributions.

This monograph is the first unified treatment of an indispensable technique for comparing statistical tests, especially in nonparametric statistics. It presents powerful new methods to evaluate explicitly different kinds of efficiencies. Many Russian results are published here for the first time in English.

Yakov Nikitin graduated from the University of St.Petersburg in 1968. He is currently the Head of Department of Probability and Statistics in this University. He is the author of more than 120 publications and a monograph entitled Asymptotic Efficiency of Nonparametric Tests (Cambridge, 1995). He is a Fellow of the Institute of Mathematical Statistics (2002).