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Simultaneous selection and estimation in general linear models. (English) Zbl 0992.62022
Summary: The problem of selecting the largest treatment parameter, and simultaneously estimating the selected treatment parameter, in a general linear model, is considered in the decision theoretic Bayes approach. Both cases, where the error variance is known or unknown, are included. Bayes decision rules are derived for noninformative priors and for normal priors. The problem of finding Bayes designs, i.e. designs that have minimum Bayes risk within a given class of designs, is also discussed.

##### MSC:
 62F07 Statistical ranking and selection procedures 62C10 Bayesian problems; characterization of Bayes procedures
##### Keywords:
nuisance parameter; Bayes rule; optimum Bayes design
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##### References:
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