Inference and Asymptotics

Capa
CRC Press, 1 de mar de 1994 - 360 páginas
Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.
 

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Conteúdo

Preface
7
Some general concepts
14
Firstorder theory
80
preliminaries and motivations
119
Some tools of higherorder theory
143
likelihood combinants
172
some further results and tools
225
Various notions of pseudolikelihood and higherorder
261
Further aspects
298
References
332
Author index
351
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