Minimax Multiple t-Tests for Comparing k Normal Populations with a Control.
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1984
- Accession Number
- ADA148306
Entities
People
- K. J. Miescke
- Sumedha Gupta
Organizations
- Purdue University