Mathematical Statistics: A Decision Theoretic Approach
Academic Press, 1967 - Mathematical statistics - 396 pages
Game theory and decision theory; The main theorems of decision theory; Distributions and sufficient statistics; Invariant statistical decision problems; Testing hypotheses; Multiple decision problems; Sequential decision problems.
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Game Theory and Decision Theory
The Main Theorems of Decision Theory
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admissible Bayes risk Bayes rule Bayes with respect best invariant estimate chooses completing the proof conditional distribution confidence sets consider convex set decision problem decision theory defined Definition denoted density distribution function equivalent example Exercise exists expected loss exponential family family of confidence family of distributions finite given X1 group 9 Hence hypothesis implies independent inequality integral invariant decision rule Lemma Let X1 linear locally best location parameter loss function matrix maximal invariant minimal minimax rule nonnegative nonrandomized decision rules nonrandomized rules normal distribution observation power function prior distribution probability mass function problem is invariant random variable real line risk function risk set rule with respect satisfied Section sequential decision rule Show SPRT statistician stopping rule sufficient statistic Suppose terminal decision rule Theorem tion transformations two-sided test variance vector zero