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On closed form semiparametric estimators for measurement error models. (English) Zbl 1087.62047
Summary: We examine the locally efficient semiparametric estimator proposed by A. A. Tsiatis and Y. Ma [Biometrika 91, 835–848 (2004; Zbl 1064.62034)] 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 of L. A. Stefanski and R. J. Carroll [ibid. 74, 703–716 (1987; Zbl 0632.62052)]. We also demonstrate how other consistent semiparametric estimators naturally emerge. The method is used in an extension of the usual generalized linear models.

62G05 Nonparametric estimation
62J12 Generalized linear models (logistic models)
62B05 Sufficient statistics and fields