
Principles of Statistical Inference from a Neo-Fisherian Perspective
- 556 pages
- English
- PDF
- Available on iOS & Android
Principles of Statistical Inference from a Neo-Fisherian Perspective
About this book
In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term “neo-Fisherian” highlights this.
After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).
The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.
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Table of contents
- CONTENTS
- PREFACE
- LIST OF SYMBOLS
- CHAPTER 1 STATISTICAL MODELS
- CHAPTER 2 DATA AND MODEL REDUCTION
- CHAPTER 3 SURVEY OF SOME BASIC CONCEPTS AND TECHNIQUES
- CHAPTER 4 NUISANCE PARAMETERS AND PSEUDO-LIKELIHOODS
- CHAPTER 5 EXPONENTIAL FAMILIES
- CHAPTER 6 EXPONENTIAL DISPERSION FAMILIES AND GENERALIZED LINEAR MODELS
- CHAPTER 7 GROUP FAMILIES
- CHAPTER 8 ASYMPTOTIC METHODS: INTRODUCTION AND ELEMENTARY TECHNIQUES
- CHAPTER 9 ASYMPTOTIC EXPANSIONS FOR STATISTICS
- CHAPTER 10 ASYMPTOTIC EXPANSIONS FOR DISTRIBUTIONS
- CHAPTER 11 LIKELIHOOD AND HIGHER-ORDER ASYMPTOTICS
- APPENDIX A LAWS OF LARGE NUMBERS AND CENTRAL LIMIT THEOREMS
- APPENDIX B ASYMPTOTIC DISTRIBUTION OF EXTREMES
- APPENDIX C PARAMETRIC INFERENCE: BASIC TERMINOLOGY
- APPENDIX D RELATIONS BETWEEN THE FREQUENCY-DECISION AND FISHERIAN PARADIGMS
- REFERENCES
- AUTHOR INDEX
- SUBJECT INDEX