Contiguity of Probability Measures: Some Applications in Statistics

Contiguity of Probability Measures: Some Applications in Statistics

by George G. Roussas
     
 

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ISBN-10: 0521083540

ISBN-13: 9780521083546

Pub. Date: 10/05/1972

Publisher: Cambridge University Press

This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important

Overview

This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow.

Product Details

ISBN-13:
9780521083546
Publisher:
Cambridge University Press
Publication date:
10/05/1972
Series:
Cambridge Tracts in Mathematics and Mathematical Physics
Pages:
262

Table of Contents

1. On the concept of contiguity and related theorems; 2. Asymptotic expansion and asymptotic distribution of likelihood functions; 3. Approximation of a given family of probability measures by an exponential family - asymptotic sufficiency; 4. Some statistical applications: AUMP and AUMPU tests for certain testing hypotheses problems; 5. Some statistical applications: asymptotic efficiency of estimates; 6. Multiparameter asymptotically optimal tests.

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