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Invariant prediction regions with smallest expected measure

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
18
Issue
1
Identifiers
DOI: 10.1016/0047-259x(86)90063-1
Keywords
  • Minimax
  • Multivariate Regression
  • Tolerance Region

Abstract

Abstract A method is given for constructing a prediction region having smallest expected measure within the class of invariant level β 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 satisfied the Hunt-Stein Condition, the optimal invariant prediction region minimizes the maximum expected measure among all level β 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.

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