## The Annals of Statistics

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

### 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

#### 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.