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December, 1993 Probability-Centered Prediction Regions
Rudolf Beran
Ann. Statist. 21(4): 1967-1981 (December, 1993). DOI: 10.1214/aos/1176349405

Abstract

Consider the problem of constructing a prediction region $D_n$ for a potentially observable variable $X$ on the basis of a learning sample of size $n$. Usually, the requirement that $D_n$ contain $X$ with probability $\alpha$, conditionally on the learning sample, does not uniquely determine $D_n$. This paper develops a general probability-centering concept for prediction regions that extends to vector-valued or function-valued $X$ the classical notion of an equal-tailed prediction interval. The dual requirements of probability centering and specified coverage probability determine $D_n$ uniquely. Several examples illustrate the scope and consequences of the proposed centering concept.

Citation

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Rudolf Beran. "Probability-Centered Prediction Regions." Ann. Statist. 21 (4) 1967 - 1981, December, 1993. https://doi.org/10.1214/aos/1176349405

Information

Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0789.62070
MathSciNet: MR1245776
Digital Object Identifier: 10.1214/aos/1176349405

Subjects:
Primary: 62M20
Secondary: 62G09

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 4 • December, 1993
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