Information and exponential families: in statistical theory

Table of Contents:

CHAPTER 1 Introduction

1.1. Introductory remarks and outline
1.2. Some mathematical prerequisites
1.3. Parametric models

PART I Lods functions and inferential separation

CHAPTER 2 Likelihood and Plausibility

2.1. Universality
2.2. Likelihood functions and plausibility functions
2.3. Complements
2.4. Notes

CHAPTER 3 Sample-Hypothesis Duality and Lods Functions

3.1. Lods functions
3.2. Prediction functions
3.3. Independence
3.4. Complements
3.5. Notes

CHAPTER 4 Logic of Inferential Separation. Ancillarity and Sufficiency

4.1. On inferential separation. Ancillarity and sufficiency
4.2. B-sufficiency and B-ancillarity
4.3. Nonformation
4.4. S-, G-, and M-ancillarity and -sufficiency
4.5. Quasi-ancillarity and Quasi-sufficiency
4.6. Conditional and unconditional plausibility functions
4.7. Complements
4.8. Notes

PART II Convex analysis, unimodality, and Laplace transforms

CHAPTER 5 Convex Analysis

5.1. Convex sets
5.2. Convex functions
5.3. Conjugate convex functions
5.4. Differential theory
5.5. Complements

CHAPTER 6 Log-Concavity and Unimodality

6.1. Log-concavity
6.2. Unimodality of continuous-type distributions
6.3. Unimodality of discrete-type distributions
6.4. Complements

CHAPTER 7 Laplace Transforms

7.1. The Laplace transform
7.2. Complements

PART III Exponential families

CHAPTER 8 Introductory Theory of Exponential Families

8.1. First properties
8.2. Derived families
8.3. Complements
8.4. Notes

CHAPTER 9 Duality and Exponential Families

9.1. Convex duality and exponential families
9.2. Independence and exponential families
9.3. Likelihood functions for full exponential families
9.4. Likelihood functions for convex exponential families
9.5. Probability functions for exponential families
9.6. Plausibility functions for full exponential families
9.7. Prediction functions for full exponential families
9.8.Complements
9.9. Notes

CHAPTER 10 Inferential Separation and Exponential Families

10.1. Quasi-ancillarity and exponential families
10.2. Cuts in general exponential families
10.3. Cuts in discrete-type exponential families
10.4. S-ancillarity and exponential families
10.5. M-ancillarity and exponential families

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.


(http://as.wiley.com/WileyCDA/WileyTitle/productCd-111885750X.html)