统计学经典 Mathematical Statistics: A Decision Theoretic Approach by Thomas S. F

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Mathematical Statistics: A Decision Theoretic Approach
by Thomas S. Ferguson

Chapter 1. Game Theory and Decision Theory

• Basic Elements
• A Comparison of Game Theory and Decision Theory
• Decision Function; Risk Function
• Utility and Subjective Probability
• Randomization
• Optimal Decision Rules
• Geometric Interpretation for Finite Theta
• The Form of Bayes Rules for Estimation Problems
  

本帖隐藏的内容

Chapter 2. The Main Theorems of Decision Theory

• Admissibility and Completeness
• Decision Theory
• Admissibility of Bayes Rules
• Basic Assumptions
• Existence of Bayes Decision Rules
• Existence of a Minimal Complete Class
• The Separating Hyperplane Theorem
• Essential Completeness of the Class of Nonrandomized Decision Rules
• The Minimax Theorem
• The Complete Class Theorem
• Solving for Minimax Rules
  

Chapter 3. Distributions and Sufficient Statistics

• Useful Univariate Distributions
• The Multivariate Normal Distribution
• Sufficient Statistics
• Essentially Complete Classes of Rules Based on Sufficient Statistics
• Exponential Families of Distributions
• Complete Sufficient Statistics
• Continuity of the Risk Function
  

Chapter 4. Invariant Statistical Decision Problems

• Invariant Decision Problems
• Invariant Decision Rules
• Admissible and Minimax Invariant Rules
• Location and Scale Parameters
• Minimax Estimates of Location Parameters
• Minimax Estimates for the Parameters of a Normal Distribution
• The Pitman Estimate
• Estimation of a Distribution Function
  

Chapter 5. Testing Hypotheses

• The Neyman-Pearson Lemma
• Uniformly Most Powerful Tests
• Two-Sided Tests
• Uniformly Most Powerful Unbiased Tests
• Locally Best Tests
• Invariance in Hypothesis Testing
• The Two-Sample Problem
• Confidence Sets
• The General Linear Hypothesis
• Confidence Ellipsoids and Multiple Comparisons
  

Chapter 6. Multiple Decision Problems

• Monotone Multiple Decision Problems
• Bayes Rules in Multiple Decision Problems
• Slippage Problems
  

Chapter 7. Sequential Decision Problems

• Sequential Decision Rules
• Bayes and Minimax Sequential Decision Rules
• Convex Loss and Sufficiency
• Invariant Sequential Decision Problems
• Sequential Tests of a Simple Hypothesis Against a Simple Alternative
• The Sequential Probability Ratio Test
• The Fundamental Identity of Sequential Analysis
  

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关键词：Mathematical mathematica Statistics Mathematic Theoretic 经典 统计学 数理 决策理论 Ferguson

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