Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.

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Information

Publisher

Academic Press

Year

2014

ISBN

9781483221236

Topic

Matemáticas

Subtopic

Probabilidad y estadística

Front Cover
Mathematical Statistics: A Decision Theoretic Approach
Copyright Page
Table of Contents
Preface
CHAPTER 1. Game Theory and Decision Theory
CHAPTER 2. The Main Theorems of Decision Theory
CHAPTER 3. Distributions and Sufficient Statistics
CHAPTER 4. Invariant Statistical Decision Problems
CHAPTER 5. Testing Hypotheses
CHAPTER 6. Multiple Decision Problems
CHAPTER 7. Sequential Decision Problems
References
Index