Mathematical Statistics: A Decision Theoretic ApproachGame 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. |
Contents
Contents | 1 |
The Main Theorems of Decision Theory | 54 |
Distributions and Sufficient Statistics | 98 |
Copyright | |
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Common terms and phrases
a₁ admissible Bayes risk Bayes rule Bayes with respect best invariant estimate chooses completing the proof conditional distribution confidence sets consider convex set decision problem defined Definition denoted density example Exercise exists exponential family family of confidence family of distributions finite fo(x given group G H₁ Hence hypothesis independent integral invariant decision rule invariant rule Lemma let L(0 Let X1 linear location parameter loss function matrix maximal invariant minimal minimax rule Neyman-Pearson lemma nonnegative nonrandomized decision rules nonrandomized rules normal distribution observation p₁ 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 statistician stopping rule subset sufficient statistic Suppose Theorem tion transformations truncated UMP unbiased unbiased test variance vector X₁ zero σ²