The Annals of Statistics

The Nonexistence of 100$(1 - \alpha)$% Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models

Leon Jay Gleser and Jiunn T. Hwang

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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.

Article information

Source
Ann. Statist. Volume 15, Number 4 (1987), 1351-1362.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350597

Digital Object Identifier
doi:10.1214/aos/1176350597

Mathematical Reviews number (MathSciNet)
MR913561

JSTOR
links.jstor.org

Subjects
Primary: 62F25: Tolerance and confidence regions
Secondary: 62F11 62H12: Estimation 62H99: None of the above, but in this section

Keywords
Confidence intervals confidence regions coverage estimation of mixing proportions expected length errors-in-variables regression inverse regression calibration principal components analysis von Mises distribution on the circle

Citation

Gleser, Leon Jay; Hwang, Jiunn T. The Nonexistence of 100$(1 - \alpha)$% Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models. Ann. Statist. 15 (1987), no. 4, 1351--1362. doi:10.1214/aos/1176350597. http://projecteuclid.org/euclid.aos/1176350597.


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