SEMINARS
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Spring 2006
STATISTICS
COLLOQUIUM
Wednesday, April 19, 2006
3:30-4:00—Refreshments
4:00-5:00—Talk
Yost Hall, Room 101
Xiaofeng Wang, PhD
Cleveland Clinic Foundation, Department of Quantitative Health Sciences
Nonparametric Regression with Measurement Errors in Predictors
Work done jointly with Dr. Jiayang Sun
Abstract
An interesting and challenging nonparametric regression problem is the estimation of a
regression function when the predictor variables are measured with errors. This occurs often
in biometry, epidemiology and economics. Conventional nonparametric regression estimators
that ignore measurement errors can be misleading. There have been two lines of attack to
correct for measurement errors; see, for example, the Fourier deconvolution method by Fan
& Truong (1993) and Simulation-extrapolation (SIMEX) by Carroll et al. (1999). In this
paper, we introduce our new nonparametric procedure for estimating the regression function
when there are errors in predictors. The resulting estimators are stable and easy to compute
– there are no Fourier transformations needed in the calculation and there is no simulation
model to assume as it is in SIMEX. They can be also used in the case that measurement
errors are non-homogeneous. The form of our new estimators has some similarity to the
Shannon Sampling Procedure and is hence named Shannon Weighted Average Procedure
(SWAP). Further, the SWAP estimators have faster convergence rates than those of Fourier
type estimators. Some simulation studies and data applications will also be presented.
Key words: Measurement errors, Nonparametric regression, SWAP estimator, Fourier
deconvolution, SIMEX.
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