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October, 1972 Sharp One-Sided Confidence Bounds Over Positive Regions
Robert Bohrer, George K. Francis
Ann. Math. Statist. 43(5): 1541-1548 (October, 1972). DOI: 10.1214/aoms/1177692386


The paper develops one-sided analogs to Scheffe's two-sided confidence bounds for a function $f(\mathbf{x}), \mathbf{x} \in R^n$. If the domain $X\ast$ of $f$ is a subset of $R_+^n = \{\mathbf{x}: x_i \geqq 0, \forall i\}$, then the upper Scheffe bounds are conservative upper confidence bounds, which can be sharpened, often to great practical advantage. This sharpening, accomplished by a non-trivial extension of Scheffe's method, is developed by the geometry-probability argument of Section 2. Section 3 derives coverage probabilities for general 2- and 3-parameter functions and illustrates savings by the sharp bounds in two examples.


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Robert Bohrer. George K. Francis. "Sharp One-Sided Confidence Bounds Over Positive Regions." Ann. Math. Statist. 43 (5) 1541 - 1548, October, 1972.


Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0396.62024
MathSciNet: MR346994
Digital Object Identifier: 10.1214/aoms/1177692386

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 5 • October, 1972
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