Yao, WeixinLindsay, Bruce G.Li, Runze2012-11-082012-11-082012-11-08http://hdl.handle.net/2097/14923A local modal estimation procedure is proposed for the regression function in a nonparametric regression model. A distinguishing characteristic of the proposed procedure is that it introduces an additional tuning parameter that is automatically selected using the observed data in order to achieve both robustness and efficiency of the resulting estimate. We demonstrate both theoretically and empirically that the resulting estimator is more efficient than the ordinary local polynomial regression estimator in the presence of outliers or heavy tail error distribution (such as t-distribution). Furthermore, we show that the proposed procedure is as asymptotically efficient as the local polynomial regression estimator when there are no outliers and the error distribution is a Gaussian distribution. We propose an EM type algorithm for the proposed estimation procedure. A Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed method. The simulation results confirm the theoretical findings. The proposed methodology is further illustrated via an analysis of a real data example.This is an electronic version of an article published in Yao, W., Lindsay, B. G., & Li, R. (2012). Local modal regression. Journal of Nonparametric Statistics, 24(3), 647-663. Journal of Nonparametric Statistics is available online at: http://www.tandfonline.com/doi/full/10.1080/10485252.2012.678848Adaptive regressionLocal polynomial regressionM-estimatorModal regressionRobust nonparametric regressionArticle (author version)