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December, 1987 The Nonexistence of 100$(1 - \alpha)$% Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models
Leon Jay Gleser, Jiunn T. Hwang
Ann. Statist. 15(4): 1351-1362 (December, 1987). DOI: 10.1214/aos/1176350597

Abstract

Confidence intervals are widely used in statistical practice as indicators of precision for related point estimators or as estimators in their own right. In the present paper it is shown that for some models, including most linear and nonlinear errors-in-variables regression models, and for certain estimation problems arising in the context of classical linear models, such as the inverse regression problem, it is impossible to construct confidence intervals for key parameters which have both positive confidence and finite expected length. The results are generalized to cover general confidence sets for both scalar and vector parameters.

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Leon Jay Gleser. Jiunn T. Hwang. "The Nonexistence of 100$(1 - \alpha)$% Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models." Ann. Statist. 15 (4) 1351 - 1362, December, 1987. https://doi.org/10.1214/aos/1176350597

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0638.62035
MathSciNet: MR913561
Digital Object Identifier: 10.1214/aos/1176350597

Subjects:
Primary: 62F25
Secondary: 62F11, 62H12, 62H99

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December, 1987
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