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December, 1984 Average Width Optimality of Simultaneous Confidence Bounds
Daniel Q. Naiman
Ann. Statist. 12(4): 1199-1214 (December, 1984). DOI: 10.1214/aos/1176346787

Abstract

Simultaneous confidence bounds for multilinear regression functions over subregions $X$ of Euclidean space are defined to be $\mu$-optimal in a class of bounds $C$, if they minimize average width with respect to $\mu$ over $X$, among all bounds in $C$ with equal coverage probability. We show that for certain simultaneous confidence bounds we can find a measure $\mu$ relative to which the bounds are $\mu$-optimal in $C$, where $C$ is a large class of bounds. Such results are obtained for bounds over finite sets, and for bounds for simple linear regression functions over finite intervals.

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Daniel Q. Naiman. "Average Width Optimality of Simultaneous Confidence Bounds." Ann. Statist. 12 (4) 1199 - 1214, December, 1984. https://doi.org/10.1214/aos/1176346787

Information

Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0554.62029
MathSciNet: MR760683
Digital Object Identifier: 10.1214/aos/1176346787

Subjects:
Primary: 62J15
Secondary: 62C07, 62J07

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 4 • December, 1984
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