The Annals of Statistics

Average Width Optimality of Simultaneous Confidence Bounds

Daniel Q. Naiman

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1199-1214.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346787

Digital Object Identifier
doi:10.1214/aos/1176346787

Mathematical Reviews number (MathSciNet)
MR760683

Zentralblatt MATH identifier
0554.62029

JSTOR
links.jstor.org

Subjects
Primary: 62J15: Paired and multiple comparisons
Secondary: 62J07: Ridge regression; shrinkage estimators 62C07: Complete class results

Keywords
Simultaneous confidence bounds multilinear regression analysis of variance

Citation

Naiman, Daniel Q. Average Width Optimality of Simultaneous Confidence Bounds. Ann. Statist. 12 (1984), no. 4, 1199--1214. doi:10.1214/aos/1176346787. https://projecteuclid.org/euclid.aos/1176346787


Export citation