Abstract
In this chapter we deal with a regression model in which there is Gaussian error in the regressor and the response variable has an exponential distribution. We consider three methods of estimation: Sufficiency estimator, Conditional Score estimators developed by Stefanski and Carroll (Biometrika 74, 703–716 1987), and Corrected Score estimator developed by Stefanski (Commun. Stat. Theory Methods 18, 4335–4358 1989) and Nakamura (Biometrika 77, 127–132 1990). We have written explicitly the estimating equations for these estimators. Sufficiency and Corrected Score estimators were compared numerically.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Carroll, R.J., Ruppert, D., Stefanski, L.A., Crainiceanu, C.M.: Measurement Error in Nonlinear Models—A Modern Perspective. Chapman & Hall, Boca Raton (2006)
Greene, W.H.: Econometric Analysis. Prentice-Hall, New Jersey (2011)
Kukush, A., Schneeweiss, H.: Comparing different estimators in a nonlinear measurement error model. Part I. Math. Methods Stat. 14, 53–79 (2005)
Lehmann, E.L., Casella, G.: Theory of Point Estimation. Springer, New York (1998)
Nakamura, T.: Corrected-score functions for error-in-variables models. Biometrika 77, 127–132 (1990)
Shao, J., Zhang, H.: Lecture Notes for Statistics 709. University of Wisconsin. http://www.stat.wisc.edu/~doksum (2008). Accessed 13 July 2013
Stefanski, L.A.: Unbiased estimation of nonlinear function of a normal mean with application to measurement error model. Commun. Stat. Theory Methods 18, 4335–4358 (1989)
Stefanski, L.A., Carroll, R.J.: Conditional scores and optimal scores for generalized linear measurement-error models. Biometrika 74, 703–716 (1987)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Shklyar, S. (2014). Conditional Estimators in Exponential Regression with Errors in Covariates. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-03512-3_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03511-6
Online ISBN: 978-3-319-03512-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)