The Annals of Statistics

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

Longcheen Huwang

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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

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

First available in Project Euclid: 17 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F25: Tolerance and confidence regions
Secondary: 62J99: None of the above, but in this section 62E99: None of the above, but in this section

Errors-in-variables confidence level asymptotically honest confidence set converge normally in all parameters


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.

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  • Anderson, T. W. (1984). Estimating linear statistical relationships. Ann. Statist. 12 1-45.
  • Chung, K. L. (1974). A Course in Probability Theory, 2nd ed. Academic Press, New York.
  • Creasy, M. A. (1956). Confidence limits for the gradient in the linear functional relationship. J. Roy. Statist. Soc. Ser. B 18 65-69.
  • Fuller, W. A. (1987). Measurement Error Models. Wiley, New York.
  • Gleser, L. J. and Hwang, J. T. (1987). The nonexistence of 100 1 % confidence sets of finite expected diameter in errors-in-variables and related models. Ann. Statist. 15 1351- 1362.
  • Huwang, L. (1991). Good coverage probability confidence sets in linear errors-in-variables models. Ph.D. dissertation, Statistics Center, Cornell Univ.
  • Hwang, J. T. (1995). Fieller's problems and resampling techniques. Statistica Sinica 5 161-171.
  • Kendall, M. G. and Stuart, A. (1979). The Advanced Theory of Statistics 2, 4th ed. Hafner, New York.
  • Li, K. C. (1989). Honest confidence regions for nonparametric regression. Ann. Statist. 17 1001- 1008.
  • Madansky, A. (1959). The fitting of straight lines when both variables are subject to error. J. Amer. Statist. Assoc. 54 173-205.
  • Moran, P. A. P. (1971). Estimating structural and functional relationships. J. Multivariate Anal. 1 232-255.
  • Reiersol, O. (1950). Identifiability of a linear relation between variables which are subject to error. Econometrica 18 375-389.