Minimax Multiple t-Tests for Comparing k Normal Populations with a Control.
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
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Let Pi sub 1,..., Pi sub k be k normal populations with unknown means Theta sub 1,..., Theta sub k, and a common unknown variance Sigma squared 2 or 0. Based on independent samples of sizes n sub 1,..., n sub k, the populations are to be partitioned into two sets, where the first one contains all Pi sub i with Theta sub i or theta sub 0, and where the other one contains the rest. At first it is assumed that Theta sub 0 is known. Under an additive a sub i -b sub i loss function a minimax procedure is derived which is of a simple natural form. The proof of minimaxity makes use of the Bayes approach and involves a sequence of nonsymmetric priors, which play a similar role as a least favorable prior in simpler problems. Analogous results are presented for the case that Theta sub 0 is not known. In this case, a control normal population is assumed to exist from which an additional sample of size n sub 0 can be drawn. Author
- Statistics and Probability