Nonparametric Regression In The Presence Of Measurement Error

We introduce a nonparametric regression estimator that is consistent in the presence of measurement error in the explanatory variable when one repeated observation of the mismeasured regressor is available. The approach taken relies on a useful property of the Fourier transform, namely, its ability to convert complicated integral equations into simple algebraic equations. The proposed estimator is shown to be asymptotically normal, and its rate of convergence in probability is derived as a function of the smoothness of the densities and conditional expectations involved. The resulting rates are often comparable to kernel deconvolution estimators, which provide consistent estimation under the much stronger assumption that the density of the measurement error is known. The finite-sample properties of the estimator are investigated through Monte Carlo experiments.This work was made possible in part through financial support from the National Science Foundation via grant SES-0214068. The author is grateful to the referees and the co-editor for their helpful comments.