Information and Exponential Families In Statistical Theory [Hardcover]

First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.CHAPTER 1 INTRODUCTION 1

1.1 Introductory remarks and outline 1

1.2 Some mathematical prerequisites 2

1.3 Parametric models 7

Part I Lods functions and inferential separation

CHAPTER 2 LIKELIHOOD AND PLAUSIBILITY 11

2.1 Universality 11

2.2 Likelihood functions and plausibility functions 12

2.3 Complements 16

2.4 Notes 16

CHAPTER 3 SAMPLE-HYPOTHESIS DUALITY AND LODS FUNCTIONS 19

3.1 Lods functions 20

3.2 Prediction functions 23

3.3 Independence 26

3.4 Complements 30

3.5 Notes 31

CHAPTER 4 LOGIC OF INFERENTIAL SEPARATION. ANCILLARITY AND SUFFICIENCY 33

4.1 On inferential separation. Ancillarity and sufficiency 33

4.2 B-sufficiency and B-ancillarity 38

4.3 Nonformation 46

4.4 S-, G-, and M-ancillarity and -sufficiency 49

4.5 Quasi-ancillarity and Quasi-sufficiency 57

4.6 Conditional and unconditional plausibility functions 58

4.7 Complements 62

4.8 Notes 68

Part II Convex analysis, unimodal“'