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3 BAYES PROCEDURES FOR SHIFT ALTERNATIVES
1+ BAYES PROCEDURES FOR DISTRIBUTIONFREE ALTERNATIVES
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admissible Bayes procedure takes Bayes risk Bayes rule Bayes solution Bayes statistic Bayes two-decision procedure Bayes with respect Beta distribution Bp(s chapter Classical rank procedures classical rank tests combined sample considered continuous function converges in probability corresponding to values decision problem denote density f disjoint sets dW(B equation exponential distribution F and G Fisher gives values Hoeffding statistic hypothesis G(x Lehmann alternatives Let AQ likelihood LMP procedure LMP test locally most powerful Mann-Whitney maximum likelihood mixture of Lehmann normal distribution order statistics orders the rank parameter pooled sample prior distribution prior probability vectors problem is distribution-free procedure is equivalent Proof random variable rank orders corresponding rank-order data real line real numbers risk function Savage statistic Saxena section 2.2 shift alternatives strictly increasing function supportive of G Suppose Terry tQ is Bayes two-decision problem u(si uniformly most powerful values of B„(s|2 values of BL(z various prior probability Yates