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European Association of Methodology

Department of methodology and evaluation research

Jena University


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Contributions: Abstract

Comparison of three estimators in the Poisson errors-in-variables model

Sergiy Shklyar Hans Schneeweiss
Taras Shevchenko UniversityUniversity of Munich
UkraineGermavy

The structural Poisson regression measurement error model is considered. The measurement error is assumed to be normally distributed variable with known variance. Unobserved regressor is a normal variable with unknown parameters.

Three consistent estimators are studied: the exact corrected(functional) estimator, the adjusted for attenuation naive (simple structural) estimator, and the quasi-likelihood (structural weighted least squares) estimator.

The uniqueness of the solution to the estimation equation for the adjusted naive and quasu-likelihood estimators is proved.The asymptotic covariance matrices of all three estimators are compared.The most asymptotically accurate estimator is quasi-likelihood one,and the least accurate is the exact corrected estimator.

References

A. Kukush, H. Schneeweiss, R. Wolf (2002). Comparing different estimators in a nonlinear measurement error model.DP244, SFB 386.

A. Kukush, S. Shklyar (2002).Comparison of three estimators in Poisson errors-in-variablesmodel with one covariate.DP294, SFB 386.

S. Shklyar, H. Schneeweiss (2002).A comparison of asymptotic covariance matrices of three consistentestimators in the Poisson regression model with measurement errors.DP283, SFB 386.

Christopher C. Heyde (1997).Quasi-likelihood and its application: A general approach tooptimal parameter estimation. Springer.

R.J. Carrol, D. Ruppert, L.A. Stefanski (1995).Measurement error in nonlinear models.Chapman & Hall, London.