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.

Keywords:

• multivariate mean–variance model
• measurement errors
• zero-inflated Poisson model
• quasi-score
• corrected score

MSC 2000 :

• 62J05
• 62H12
• 62F12

Acknowledgements

Support by the German Research Foundation and by the Alexander von Humboldt Foundation is gratefully acknowledged. A. Kukush is supported as well by the Swedish Institute grant SI-01424/2007.