Abstract
It is well known that for one-dimensional normal EV regression modelX = x + u,Y = α + βx +e, wherex,u,e are mutually independent normal variables andEu =Ee = 0, the regression parameters α and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for α and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of α and β exist, and the form of the MVUE of α and β are also given.
Similar content being viewed by others
References
Adcook, R. J., Note on the method of least squares, Analyst, 1877, 4: 183–184.
Adcook, R. J., A problem in least squares, Analyst, 1878, 5: 53–54.
Kendall, M., Stuart, A., The Advanced Theory of Statistics, Vol. 2, 4th ed., London: Charles Griffin & Company Limited, 1979.
Fuller, W. A., Measurement Error Models, New York: John Wiley, 1987.
Cheng, C. L., Van Ness, J. W., Statistical Regression with Measurement Error, London: Arnold, 2000.
Reiersol, O., Identifiability of a linear relation between variables which are subjected to errors, Econometrica, 1950, 18: 375–389.
Bunke, H., Bunke, O., Nonlinear Regression, Functional Relations and Robust Methods, New York: John Wiley, 1989.
Hsiao, C., Consistent estimation for some non-linear error-in-variables methods, J. Econometrics, 1989, 41: 159–185.
Chen, X. R., Introduction to Mathematical Statistical (in Chinese), Beijing: Science Press, 1982.
Crammer, H., Mathematical Methods of Statistics, Princeton: Princeton Univ. Press, 1946.
Lavrenev, M. A., Sambat, B. A., Methods of Complex Variable (translated by Shi, X. L., Xia, D. Z.,), Beijing: High Education Press, 1956.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jixue, L., Xiru, C. Existence of unbiased estimate of regression parameters in simple linear EV models. Sci. China Ser. A-Math. 48, 915–928 (2005). https://doi.org/10.1007/BF02879074
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02879074