Local polynomial regression in the presence of covariate measurement error: An improved SIMEX estimator

This dissertation improves the performance and theoretical understanding of the local polynomial/simulation extrapolation (SIMEX) estimator for the problem of non-parametric regression in the presence of covariate measurement error. The improvements come from using new theoretical results to restructure the bandwidth selection method. We test the performance of our estimator using a Monte Carlo simulation experiment and find that it performs much better than the current local polynomial/SIMEX estimator and nearly as well as the "Structural Penalized Regression Spline" estimator of Carroll, Maca, and Ruppert (1999). In addition to formulating and testing the new estimator, we also quantify the cost of ignoring the covariate measurement error in this problem by deriving the asymptotic conditional bias and variance of the local polynomial estimator that ignores measurement error. These results are used to derive the asymptotic conditional bias and variance of the local polynomial/SIMEX estimator.