The Annals of Statistics

Optimal Simultaneous Confidence Bounds

Daniel Q. Naiman

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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.

Article information

Source
Ann. Statist., Volume 12, Number 2 (1984), 702-715.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346516

Digital Object Identifier
doi:10.1214/aos/1176346516

Mathematical Reviews number (MathSciNet)
MR740922

Zentralblatt MATH identifier
0546.62046

JSTOR
links.jstor.org

Subjects
Primary: 62J15: Paired and multiple comparisons
Secondary: 62J10: Analysis of variance and covariance 62C07: Complete class results

Keywords
Simultaneous confidence bounds multilinear regression analysis of variance

Citation

Naiman, Daniel Q. Optimal Simultaneous Confidence Bounds. Ann. Statist. 12 (1984), no. 2, 702--715. doi:10.1214/aos/1176346516. https://projecteuclid.org/euclid.aos/1176346516


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