Three estimators for the poisson regression model with measurement errors |
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Authors: | Alexander Kukush Hans Schneeweis Roland Wolf |
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Affiliation: | (1) Department of Mechanics and Mathematics, Kiev National Taras Shevchenko University, Vladimirskaya st. 64, 01033 Kiev, Ukraine;(2) Department of Statistics, Ludwig Maximilian University, Akademiestr. 1, 80799 Munich, Germany |
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Abstract: | We consider two consistent estimators for the parameters of the linear predictor in the Poisson regression model, where the covariate is measured with errors. The measurement errors are assumed to be normally distributed with known error variance σ u 2 . The SQS estimator, based on a conditional mean-variance model, takes the distribution of the latent covariate into account, and this is here assumed to be a normal distribution. The CS estimator, based on a corrected score function, does not use the distribution of the latent covariate. Nevertheless, for small σ u 2 , both estimators have identical asymptotic covariance matrices up to the order of σ u 2 . We also compare the consistent estimators to the naive estimator, which is based on replacing the latent covariate with its (erroneously) measured counterpart. The naive estimator is biased, but has a smaller covariance matrix than the consistent estimators (at least up to the order of σ u 2 ). |
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Keywords: | Poisson regression model measurement errors corrected score estimator structural quasi score estimator naive estimator |
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