Biometrika Advance Access published online on August 8, 2008
Biometrika, doi:10.1093/biomet/asn024
Articles |
Additive partial linear models with measurement errors
Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, New York 14642, U.S.A. hliang{at}bst.rochester.edu thurston{at}bst.rochester.edu
College of Engineering, Cornell University, Ithaca, New York 14853, U.S.A. dr24{at}cornell.edu tva2{at}cornell.edu
Department of Environmental Health, Harvard School of Public Health, Boston, Massachusetts 02115, U.S.A. rhauser{at}hohp.harvard.edu
Received for publication 1 December 2006. Revision received 1 January 2008.
We consider statistical inference for additive partial linear models when the linear covariate is measured with error. We propose attenuation-to-correction and simulation-extrapolation, simex, estimators of the parameter of interest. It is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing. This is an advantage of our estimator over existing backfitting-based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component to be root-n consistent. This feature stems from a decrease of the bias of the resulting estimator, which is appropriately derived using a profile procedure. A similar characteristic in semiparametric partially linear models was obtained by Wang et al. (2005). We also discuss the asymptotics of the proposed simex approach. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are applied to a dataset from a semen study.
Key Words: Backfitting • Correction-for-attenuation • Error prone • Local linear regression • Semen quality study • Semiparametric estimation • SIMEX • Undersmoothing
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