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