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Biometrika 1999 86(3):541-554; doi:10.1093/biomet/86.3.541
© 1999 by Biometrika Trust
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Nonparametric regression in the presence of measurement error

RJ CarrollA1, JD MacaA2 and D RuppertA3

A1 Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA E-mail: carroll@stat.tamu.edu A2 Department of Statistics, Novartis Pharmaceuticals Corporation, 59 Route 10, East Hanover, NJ 07936-1080, USA E-mail: jeff.maca@pharma.novartis.com A3 School of Operational Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA E-mail: davidr@orie.cornell.edu

In many regression applications the independent variable is measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different approaches to nonparametric regression. The first uses the SIMEX, simulation-extrapolation, method and makes no assumption about the distribution of the unobserved error-prone predictor. For this approach we derive an asymptotic theory for kernel regression which has some surprising implications. Penalised regression splines are also considered for fixed number of known knots. The second approach assumes that the error-prone predictor has a distribution of a mixture of normals with an unknown number of components, and uses regression splines. Simulations illustrate the results.

Key Words: Estimating equation; Local polynomial regression; Measurement error; Regression spline; Sandwich estimation; SIMEX


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