Comparison of three estimators in Poisson errors-in-variables model with one covariate

Abstract

A structural errors-in-variables model is investigated, where the response variable follows a Poisson distribution. Assuming the error variance to be known, we consider three consistent estimators and compare their relative efficiencies by means of their asymptotic covariance matrices. The comparison is made for arbitrary error variances. The structural quasi-likelihood (QL) estimator is based on a quasi score function, which is constructed from a conditional mean-variance model. The corrected estimator is based on an error-corrected likelihood score function. The alternative estimator is constructed to remove the asymptotic bias of the naive (i.e., ordinary maximum likelihood) estimator. It is shown that the QL estimator is strictly more efficient than the alternative estimator, and the latter one is strictly more efficient than the corrected estimator.