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33 reviews
ISBN 10: 1118857283
ISBN 13: 9781118857281
Author: Ole E Barndorff Nielsen
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 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
10.6 Complement
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Tags: Ole E Barndorff Nielsen, Exponential, Families
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