Modern Stochastics and Applications pp 337-349

Part of the Springer Optimization and Its Applications book series (SOIA, volume 90)

# Conditional Estimators in Exponential Regression with Errors in Covariates

Chapter

## 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.

### References

1. 1.
Carroll, R.J., Ruppert, D., Stefanski, L.A., Crainiceanu, C.M.: Measurement Error in Nonlinear Models—A Modern Perspective. Chapman & Hall, Boca Raton (2006)
2. 2.
Greene, W.H.: Econometric Analysis. Prentice-Hall, New Jersey (2011)Google Scholar
3. 3.
Kukush, A., Schneeweiss, H.: Comparing different estimators in a nonlinear measurement error model. Part I. Math. Methods Stat. 14, 53–79 (2005)
4. 4.
Lehmann, E.L., Casella, G.: Theory of Point Estimation. Springer, New York (1998)
5. 5.
Nakamura, T.: Corrected-score functions for error-in-variables models. Biometrika 77, 127–132 (1990)
6. 6.
Shao, J., Zhang, H.: Lecture Notes for Statistics 709. University of Wisconsin. http://www.stat.wisc.edu/~doksum (2008). Accessed 13 July 2013
7. 7.
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)
8. 8.
Stefanski, L.A., Carroll, R.J.: Conditional scores and optimal scores for generalized linear measurement-error models. Biometrika 74, 703–716 (1987)