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June, 1992 Controlling Conditional Coverage Probability in Prediction
Rudolf Beran
Ann. Statist. 20(2): 1110-1119 (June, 1992). DOI: 10.1214/aos/1176348673

Abstract

Suppose the variable $X$ to be predicted and the learning sample $Y_n$ that was observed are independent, with a joint distribution that depends on an unknown parameter $\theta$. A prediction region $D_n$ for $X$ is a random set, depending on $Y_n$, that contains $X$ with prescribed probability $\alpha$. In sufficiently regular models, $D_n$ can be constructed so that overall coverage probability converges to $\alpha$ at rate $n^{-r}$, where $r$ is any positive integer. This paper shows that the conditional coverage probability of $D_n$, given $Y_n$, converges in probability to $\alpha$ at a rate which usually cannot exceed $n^{-1/2}$.

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Rudolf Beran. "Controlling Conditional Coverage Probability in Prediction." Ann. Statist. 20 (2) 1110 - 1119, June, 1992. https://doi.org/10.1214/aos/1176348673

Information

Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0746.62095
MathSciNet: MR1165609
Digital Object Identifier: 10.1214/aos/1176348673

Subjects:
Primary: 62M20
Secondary: 62E20

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 2 • June, 1992
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