Optimality of quasi-score in the multivariate mean–variance model with an application to the zero-inflated Poisson model with measurement errors

Abstract

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.

Comparing the efficiency of structural and functional methods in measurement error models

“…x are unknown and have to be estimated, but they must be estimated together with β, and not in advance, [18,19]. A multivariate version of this approach has been applied to estimate a zero-inflated Poisson measurement error model [20].…”