Optimality of Quasi-Score in the multivariate mean-variance model with an application to the zero-inflated Poisson model with measurement errors

In a multivariate mean-variance model, the class of linear score
(LS) estimators based on an unbiased linear estimating function is
introduced. A special member of this class is the (extended)
quasi-score (QS) estimator. It is ``extended'' in the sense that it
comprises the parameters describing the distribution of the
regressor variables. It is shown that QS is (asymptotically) most
efficient within the class of LS estimators. An application is the
multivariate measurement error model, where the parameters
describing the regressor distribution are nuisance parameters. A
special case is the zero-inflated Poisson model with measurement
errors, which can be treated within this framework.