Open Access
Translator Disclaimer
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


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.


Download Citation

Daniel Q. Naiman. "Average Width Optimality of Simultaneous Confidence Bounds." Ann. Statist. 12 (4) 1199 - 1214, December, 1984.


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

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

Primary: 62J15
Secondary: 62C07 , 62J07

Keywords: Analysis of variance , multilinear regression , Simultaneous confidence bounds

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
Back to Top