SIMEX is a general-purpose technique for measurement error correction. There is a substantial literature on the application and theory of SIMEX for purely parametric problems, as well as for purely non-parametric regression problems, but there is neither application nor theory for semiparametric problems. Motivated by an example involving radiation dosimetry, we develop the basic theory for SIMEX in semiparametric problems using kernel-based estimation methods. This includes situations that the mismeasured variable is modeled purely parametrically, purely non-parametrically, or that the mismeasured variable has components that are modeled both parametrically and nonparametrically. Using our asymptotic expansions, easily computed standard error formulae are derived, as are the bias properties of the nonparametric estimator. The standard error method represents a new method for estimating variability of nonparametric estimators in semiparametric problems, and we show in both simulations and in our example that it improves dramatically on first order methods. We find that for estimating the parametric part of the model, standard bandwidth choices of order O(n−1/5) are sufficient to ensure asymptotic normality, and undersmoothing is not required. SIMEX has the property that it fits misspecified models, namely ones that ignore the measurement error. Our work thus also more generally describes the behavior of kernelbased methods in misspecified semiparametric problems. © 2009, Institute of Mathematical Statistics. All rights reserved.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Our research was supported by grants from the National Cancer Institute (CA57030, CA104620). Part of Carroll's research was supported by award in number KUS-CI-016-04 made by the King Abdullah University of Science and Technology (KAUST). Apanasovich's research was supported by a grant from the National Science Foundation #0707106. The work of Apanasovich and Carroll partially occurred during a visit to and with the support of the Department of Mathematics and Statistics at the University of Melbourne, and is gratefully acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.