Contiguity of Probability Measures: Some Applications in Statistics

George G. Roussas

doi:10.1017/CBO9780511804373

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.

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Contiguity of Probability Measures

Some Applications in Statistics

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Contents

Frontmatter
pp i-vi

Contents
pp vii-ix

Acknowledgement
pp x-x

Preface
pp xi-xiv

1 - On the concept of contiguity and related theorems
pp 1-40

2 - Asymptotic expansion and asymptotic distribution of likelihood functions
pp 41-66

3 - Approximation of a given family of probability measures by an exponential family – asymptotic sufficiency
pp 67-84

4 - Some statistical applications: AUMP and AUMPU tests for certain testing hypotheses problems
pp 85-127

5 - Some statistical applications: asymptotic efficiency of estimates
pp 128-166

6 - Multiparameter asymptotically optimal tests
pp 167-198

Appendix
pp 199-239

Bibliography
pp 240-245

Index
pp 246-248

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Some Applications in Statistics

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