Inference and Asymptotics PDF

Preface

Our book Asymptotic Techniques for 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.

We have attempted to follow a connected line of developments but inevitably some parts are more specialized than other. The following are some of the sections that might be largely omitted at a first reading: the later part of section 2.8, sections 3.8, 5.3-5.7, 6.3, 6.4, 13-1.6 and Chapter 9.

We are grateful to Dawn Peters and Neil Shephard for comments on some of the chapters.

Our collaboration has been supported throughout by a grant from the European Communities for which we wish to express our strong appreciation.

Susanne Slotsdal and Oddbjorg Wethelund, Aarhus University, did outstanding work typing a difficult manuscript.

Authors: D.R. Cox, O.E. Barndorff-Nielsen