The Annals of Statistics

Optimal Simultaneous Confidence Bounds

Daniel Q. Naiman

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

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