Preface

Summary

‘Although this may seem a paradox, all science is dominated by the idea of approximation.’

Bertrand Russell

This monograph represents a modest attempt on my part to introduce the concept of contiguity, elaborate on the mathematical theory behind it, and also indicate some of its statistical applications. It lays no claim in containing an exhaustive discussion of results pertaining to contiguity. In fact, there are already new results available which, however, could not have been included in this book. It is simply the result of an attempt to make the concept of contiguity and some of its statistical applications more familiar to several kinds of research workers. These include Theoretical Statisticians, Probabilists, Mathematicians whose primary interest lies in measure theory or approximation theory, and perhaps to practitioners of Statistics as well. It is my belief that contiguity deserves more attention than it has received. I hope that this monograph will be a step in that direction, anticipating the appearance of a more comprehensive treatise on the subject.

The concept of contiguity was introduced by Professor Lucien LeCam as a criterion of nearness of sequences of probability measures. In addition to its purely mathematical interest, contiguity is a powerful and very useful tool in Statistics, when one is concerned with asymptotic theory, leading to elegant derivations of the asymptotic properties of tests and estimates under less restrictive assumptions than usual.