Minimax multiple t-tests for comparing k normal populations with a control
type: Item
instance of: scholarly article
title: Minimax multiple t-tests for comparing k normal populations with a control
zbMATH Open document ID: 0573.62011
DOI: 10.1016/0378-3758(85)90065-5
author: Shanti S. Gupta
author: Klaus J. Miescke
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
review text: Let \(\pi_ 1,...,\pi_ k\) be k normal populations with unknown means \(\theta_ 1,...,\theta_ k\), and a common unknown variance \(\sigma^ 2>0\). Based on independent samples of sizes \(n_ 1,...,n_ k\), the populations are to be partitioned into two sets, where the first one contains all \(\pi_ i\) with \(\theta_ i\geq \theta_ 0\), and where the other one contains the rest. At first it is assumed that \(\theta_ 0\) is known. Under an additive \('a_ i-b_ i'\) 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 \(\theta_ 0\) is not known. In this case, a control normal population is assumed to exist from which an additional sample of size \(n_ 0\) can be drawn.
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62F07
zbMATH DE Number: 3915398
zbMATH Keywords: multiple comparisons with a control
zbMATH Keywords: simultaneous t-test
zbMATH Keywords: minimax k- sample tests
zbMATH Keywords: normal populations
zbMATH Keywords: unknown means
zbMATH Keywords: common unknown variance
zbMATH Keywords: independent samples
zbMATH Keywords: nonsymmetric priors
MaRDI profile type: Publication
full work available at URL: 0378-3758(85)90065-5
OpenAlex ID: W2080084972
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description: scientific article; zbMATH DE number 3915398