Open Access
June, 1984 Optimal Simultaneous Confidence Bounds
Daniel Q. Naiman
Ann. Statist. 12(2): 702-715 (June, 1984). DOI: 10.1214/aos/1176346516

Abstract

The notion of a "simultaneous confidence bound" is redefined by requiring a bound on the expected converge measure (ECM) instead of the coverage probability. This is analogous to a criterion introduced by Spjotvoll for defining simultaneous tests of hypotheses. Bounds which minimize certain width functionals, subject to a bound on the ECM, are characterized. For bounds on a multilinear regression function over an arbitrary subset of Euclidean space, the bounds which minimize weighted average width, among all bounds with prescribed ECM, are expressed in closed form. As a special case, we give a weight function relative to which Scheffe-type bounds are optimal.

Citation

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Daniel Q. Naiman. "Optimal Simultaneous Confidence Bounds." Ann. Statist. 12 (2) 702 - 715, June, 1984. https://doi.org/10.1214/aos/1176346516

Information

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

zbMATH: 0546.62046
MathSciNet: MR740922
Digital Object Identifier: 10.1214/aos/1176346516

Subjects:
Primary: 62J15
Secondary: 62C07 , 62J10

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

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • June, 1984
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