Local Polynomial Regression and SIMEX John Staudenmayer and David Ruppert ∗ June 6, 2003 Abstract: This paper introduces a new local polynomial estimator and develops supporting asymp- totic theory for non-parametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski’s simulation-extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by (1) using a bandwidth selection proce- dure that addresses SIMEX’s particular estimation method and (2) considers higher degree local polynomial estimators. We illustrate the accuracy of our asymptotic expressions with a Monte Carlo Study, compare our method to other estimators with a second set of Monte Carlo simulations, and apply our method to a dataset from nutritional epidemiology. SIMEX was originally developed for parametric models. Although SIMEX is, in principle, applicable to nonparametric models, a serious problem arises with SIMEX in nonparametric situations. The problem is that smoothing parameter selectors developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing. We believe that this is the first paper to address this difficulty. Keywords: Measurement Error; Kernel Smoothing Estimation; Bandwidth Selection ∗ John Staudenmayer is an Assistant Professor in the Department of Mathematics and Statistics, University of Mas- sachusetts, LGRT, Amherst, Massachusetts 01003-9305, U.S.A. (email: jstauden@math.umass.edu). David Ruppert is the Andrew Schultz, Jr. Professor of Engineering in the School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, U.S.A. Staudenmayer’s research was supported by National Institute of Envi- ronmental Health Sciences (NIEHS) training grant number ES07261 while he was a student at Cornell and National Institute of Health grant T32 ES07142-18 at Harvard School of Public Health. Ruppert’s research was supported by National Science Foundation grant DMS-9804058. 1