## Admissible Decision Rules for the Compound Decision ProblemDepartment of Statistics, Stanford University., 1973 - Bayesian statistical decision theory - 112 pages |

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### Contents

k A Convergence Theorem for the Posterior | 15 |

5 Establishing Asymptotic Optimality | 21 |

An Example | 26 |

3 other sections not shown

### Common terms and phrases

admissible rule Appendix average of unbiased Bayes estimator Bayes model Bayes risk Bayes rule Beck-Giesy theorem component problem compound decision problem compound decision rules consider continuous function converges to zero Corollary defined dg(y distribution functions Doctor of Philosophy Dominated Convergence Theorem du(g dy(g equicontinuous Establishing Asymptotic Optimality exp{v r/n finite following lemma func function of g Hannan and Robbins holds immediate consequence implies Large Numbers Law of Large Lemma 11 limsup log f(x,y)dg log J f(xJ,y)dg1 log(gf log(l-d max|dP metric space ne/m number of l's posterior probability prior distributions probability density probability distribution probability measure proof of Theorem random variable taking right hand side satisfy Section separable Banach space simple symmetric Strong Law subset sup v g tion uniformly bounded uniformly continuous function uniformly in 9 variable taking values vector wj|n wp 1 uniformly write