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The Case of Known Variance
Extensions of the Basic Model
2 other sections not shown
admissible estimator admissible in dimension admissible rules application apply Stein's asymptotically efficient rules Basu Bayes risk BB'e canonical form certainty equivalent certainty-equivalent rule change of variables Charles Stein Complete Class Theorem compute control problem cosh Yllylldy decision problem decision rule 6(y Define DEFINITION Density diffuse prior rule dn(Y Doctor of Philosophy earlier Econometrics equivalent rule error term expected value finite risk following theorem formal Bayes estimators formal Bayes procedures formal Bayes rules formula given hence implies inadmissible infinite mean square infinity integral intuition invariant Lebesgue measure Lemma likelihood function linear restrictions llyll loss function maximum likelihood estimate mean square error minimised normal distribution obtain original problem orthogonal parameter space plim prove quadratic loss risk function rule is admissible satisfy spherically symmetric Substituting thesis true value unbiased estimate unknown variance vector Zellner Zellner's rule