Invariant prediction regions with smallest expected measure
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.
scientific article; zbMATH DE number 3934216
scientific article