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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The book succeeds in bringing together a large amount of useful and interesting work.
-Short Book Reviews
The book is carefully structured. The presentation is generally graded so that motivations, concepts, and results are first discussed, at least briefly, with a minimum of technicalities, and then more complete details are given...usually illustrated with several examples. This style is very helpful and allows the casual reader to grasp the purposes and flow of the developments without requiring that every derivation be followed.
-Journal of the American Statistical Association
This is an authoritative and comprehensive book which develops its complex theoretical results in a coherent and logical manner. Anybody interested in recent developments in parametric likelihood theory should read it.
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