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Biometrika 2004 91(4):835-848; doi:10.1093/biomet/91.4.835
© 2004 by Biometrika Trust
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Locally efficient semiparametric estimators for functional measurement error models

Anastasios A. Tsiatis1 and Yanyuan Ma2

1 Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A. tsiatis{at}stat.ncsu.edu, 2 Centre for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695, U.S.A. yma{at}unity.ncsu.edu

A class of semiparametric estimators are proposed in the general setting of functional measurement error models. The estimators follow from estimating equations that are based on the semiparametric efficient score derived under a possibly incorrect distributional assumption for the unobserved ‘measured with error’ covariates. It is shown that such estimators are consistent and asymptotically normal even with misspecification and are efficient if computed under the truth. The methods are demonstrated with a simulation study of a quadratic logistic regression model with measurement error.

Key Words: Efficient score; Functional measurement error; Semiparametric estimator

Received October 2003. Revised February 2004.


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