Local polynomial regression and variable selection

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We propose a method for incorporating variable selection into local polynomial regression. This can improve the accuracy of the regression by extending the bandwidth in directions corresponding to those variables judged to be are unimportant. It also increases our understanding of the dataset by highlighting areas where these variables are redundant. The approach has the potential to effect complete variable removal as well as perform partial removal when a variable redundancy applies only to particular regions of the data. We define a nonparametric oracle property and show that this is more than satisfied by our approach under asymptotic analysis. The usefulness of the method is demonstrated through simulated and real data numerical examples.