The Theory of Statistical Decision

Key Points

• Formulate a unified mathematical framework for optimal decision-making in statistical inference under uncertainty.
• Theoretical exposition characterizing parameter spaces, decision spaces, and loss functions.
• Mathematical analysis evaluating risk functions, admissibility, and complete classes of decision rules.
• Unifies statistical hypothesis testing and parameter estimation within a comprehensive decision-theoretic framework.
• Demonstrates the fundamental relationships between minimax strategies and Bayes solutions for minimizing expected loss.