Geodesic
Efficiency comparison of two
Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 122-131.

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We study a nonlinear measurement model where the response variable has a density belonging to the exponential family. We consider two consistent estimators: Corrected Score (CS) and Quasi Score (QS) ones. Their relative e?ciency is compared with respect to asymptotic covariance matrices. We derive expansions of these matrices for small error variances. It is shown that the QS estimator is more e?cient than the CS one. The polynomial and Poisson regression models are studied in more detail.
Keywords: Errors-in-variables models, corrected score
Mots-clés : quasi score. 
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Andrii Malenko. Efficiency comparison of two. Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 122-131. http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a12/

[1] R. J. Carroll, D. Ruppert, L. A. Stefanski, Measurement Error in Nonlinear Models, Chapman and Hall, London, 1995

[2] A. Kukush, H. Schneeweiss, “Comparing different estimators in a nonlinear measurement error model. I”, Mathematical Methods of Statistics, 14 (2005), 53–79

[3] A. Kukush, A. Malenko,H. Schneeweiss, Optimality of the quasi-score-like estimator in a mean-variance model, Discussion paper 384. SFB 386, University of Munich, 2006

[4] L. A. Stefanski, “Unbiased estimation of a nonlinear function of a normal mean with application to measurement error models”, Communication in Statistics, Series A, 18 (1989), 4335–4358