The Annals of Statistics

Probability-Centered Prediction Regions

Rudolf Beran

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 1967-1981.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349405

Digital Object Identifier
doi:10.1214/aos/1176349405

Mathematical Reviews number (MathSciNet)
MR1245776

Zentralblatt MATH identifier
0789.62070

JSTOR
links.jstor.org

Subjects
Primary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 62G09: Resampling methods

Keywords
Simultaneous prediction intervals bootstrap design goals

Citation

Beran, Rudolf. Probability-Centered Prediction Regions. Ann. Statist. 21 (1993), no. 4, 1967--1981. doi:10.1214/aos/1176349405. https://projecteuclid.org/euclid.aos/1176349405


Export citation