Invariant prediction regions with smallest expected measure
type: Item
instance of: scholarly article
title: Invariant prediction regions with smallest expected measure
zbMATH Open document ID: 0583.62031
DOI: 10.1016/0047-259X(86)90063-1
author: Peter M. Hooper
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: A method is given for constructing a prediction region having smallest expected measure within the class of invariant level \(\beta\) prediction regions. The main assumptions are that the invariance group acts transitively on the parameter space and that the measure satisfies a certain invariance property. When the invariance group satisfies the Hunt-Stein condition, the optimal invariant prediction region minimizes the maximum expected measure among all level \(\beta\) prediction regions. Prediction regions are constructed for: a random variable with density of arbitrary given shape but unknown location and scale; several random vectors in a multivariate regression model; and order statistics of a sample from an unspecified continuous distribution.
Mathematics Subject Classification ID: 62F25
Mathematics Subject Classification ID: 62G15
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 3934216
zbMATH Keywords: minimax
zbMATH Keywords: tolerance region
zbMATH Keywords: prediction region
zbMATH Keywords: smallest expected measure
zbMATH Keywords: Hunt-Stein condition
zbMATH Keywords: optimal invariant prediction region
zbMATH Keywords: multivariate regression model
zbMATH Keywords: order statistics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3934216