## The Annals of Statistics

### Asymptotically honest confidence sets for structural errors-in-variables models

Longcheen Huwang

#### Abstract

The problem of constructing confidence sets for the structural errors-in-variables model is considered under the assumption that the variance of the error associated with the covariate is known. Previously proposed confidence sets for this model suffer from the problem that they all have zero confidence levels for any sample size, where the confidence level of a confidence set is defined to be the infimum of coverage probability over the parameter space. In this paper we construct some asymptotically honest confidence sets; that is, the limiting values of their confidence levels are at least as large as the nominal probabilities when the sample size goes to $\infty$. A desirable property of the proposed confidence set for the slope is also established.

#### Article information

Source
Ann. Statist., Volume 24, Number 4 (1996), 1536-1546.

Dates
First available in Project Euclid: 17 September 2002

https://projecteuclid.org/euclid.aos/1032298282

Digital Object Identifier
doi:10.1214/aos/1032298282

Mathematical Reviews number (MathSciNet)
MR1416647

Zentralblatt MATH identifier
0867.62016

#### Citation

Huwang, Longcheen. Asymptotically honest confidence sets for structural errors-in-variables models. Ann. Statist. 24 (1996), no. 4, 1536--1546. doi:10.1214/aos/1032298282. https://projecteuclid.org/euclid.aos/1032298282

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