Theory of Games and Statistical Decisions.
- 1 online resource (696 pages)
- Dover Books on Mathematics .
- Dover Books on Mathematics .
Cover Title Page Copyright Page Dedication Contents 1 Games in Normal Form 1.1 Introduction 1.2 The Concept of a Strategy 1.3 The Normal Form 1.4 Equivalent Games 1.5 Illustrative Examples 1.6 Lower and Upper Pure Value 1.7 Perfect-Information Games 1.8 Mixed Strategies 2 Values and Optimal Strategies in Games 2.1 Introduction 2.2 Convex Sets and Convex Functions 2.3 Games with a Value 2.4 S Games 2.5 Games with Convex Payoff 2.6 Extended Mixed Strategies 2.7 Solving Games 3 General Structure of Statistical Games 3.1 Introduction 3.2 The Sample Space 3.3 The Space of Pure Strategies for the Statistician 3.4 The Notion of a Random Variable 3.5 Statistician's Space of Strategies for Single Experiments 3.6 Mixed Strategies for Single-Experiment Games 3.7 Games Involving Densities 3.8 Preliminary Remarks Concerning Sequential Games 3.9 Space of Statistician's Strategies in Truncated Sequential Games 3.10 Definition of Truncated Sequential Games 3.11 Some Further Theorems on Probability 4 Utility and Principles of Choice 4.1 Introduction 4.2 Utility 4.3 Principles of Choice 5 Classes of Optimal Strategies 5.1 Introduction 5.2 Complete Classes of Strategies in S Games 5.3 The Class of Games Gη 5.4 Definition of Classes of Optimal Strategies 5.5 Set-Theoretic Relations among the Classes of Strategies 5.6 Conditions under Which the Classes of Strategies Are Complete 5.7 Completeness of the Class of Admissible Strategies 6 Fixed Sample-Size Games with Finite Ω 6.1 Introduction 6.2 Complete Classes of Strategies in Games with Finite Ω 6.3 Bayes Solutions for Finite Ω 6.4 Illustrative Examples of Fixed Sample-Size Statistical Games in Which Ω Is Finite 7 Fixed Sample-Size Games with Finite A. 7.1 Introduction 7.2 On the Equivalence of Two Methods of Randomization 7.3 Bayes Solutions in Fixed Sample-Size Games with Finite A 7.4 Fixed Sample-Size Multidecision Games Where Is the Exponential Class 7.5 Minimax Strategies in Fixed Sample-Size Multidecision Games 7.6 The Completeness of the Classes, and 7.7 Tests of Composite Hypotheses 8 Sufficient Statistics and the Invariance Principle in Statistical Games 8.1 Introduction 8.2 Partitions of Z Which Are Sufficient on 8.3 The Principle of Sufficiency 8.4 Minimal Sufficient Partitions 8.5 Sufficient Statistics for Densities 8.6 Principle of Invariance for Finite Groups 8.7 Application of the Invariance Principle to Sampling from a Finite Population 8.8 A Special Case of the Invariance Principle with an Infinite Group 9 Sequential Games 9.1 Introduction 9.2 Bayes Procedures for Sequential Games 9.3 Bayes Sequential Procedures for Constant Cost and Identically and Independently Distributed Observations 9.4 Bayes Sequential Procedures for Finite Ω 10 Bayes and Minimax Sequential Procedures When Both Ω and A Are Finite 10.1 Introduction 10.2 Method for Determining the Boundaries of the Stopping Regions for Truncated Sequential Dichotomies 10.3 Method for Determining the Boundaries of the Stopping Regions for Non-Truncated Sequential Dichotomies 10.4 Some Theory in Sequential Analysis 10.5 Approximation for and for Eω(n) 10.6 The Determination of the Stopping Regions for a Special Class of Di-chotomies 10.7 Examples of Trichotomies, i.e., Ω = (1, 2, 3), A = (1, 2, 3) 10.8 Minimax Strategies in Sequential Games with Finite Ω and A 10.9 Another Optimal Property of the Sequential-Probability Ratio Test 11 Estimation 11.1 Introduction 11.2 Bayes Estimates for Special Loss Functions. 11.3 The Translation-Parameter Problem 11.4 The Scale-Parameter Problem 11.5 Admissible Minimax Estimates for the Exponential Class 12 Comparison of Experiments 12.1 Introduction 12.2 Some Equivalent Conditions 12.3 Combinations of Experiments 12.4 Dichotomies 12.5 Binomial Dichotomies References Index.
A problem-oriented text for evaluating statistical procedures through decision and game theory. First-year graduates in statistics, computer experts and others will find this highly respected work best introduction to growing field.
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