On closed form semiparametric estimators for measurement error models

We examine the locally efficient semiparametric estimator proposed by Tsiatis and Ma (2004) in the situation when a sufficient and complete statistic exists. We derive a closed form solution and show that when implemented in generalized linear models with normal measurement error, this estimator is equivalent to the efficient score estimator in Stefanski and Carroll (1987). We also demonstrate how other consistent semiparametric estimators naturally emerge. The method is used in an extension of the usual generalized linear models. Measurement error models, semiparametric estimator.