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\noindent Statistica Sinica {\bf 16}(2006), 183-193

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\centerline{\large\bf ON CLOSED FORM SEMIPARAMETRIC ESTIMATORS}
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\centerline{\large\bf  FOR MEASUREMENT ERROR MODELS}
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\author{Yanyuan Ma and Anastasios A. Tsiatis}
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\centerline{\it Texas A{\rm \&}M University and North Carolina State}
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\noindent {\it Abstract:}
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.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Measurement error models, semiparametric estimator.\par
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