Bandwidth selection for local linear regression smoothers

Nicolas W. Hengartner, Marten H. Wegkamp and Eric Matzner‐Løber

Journal of the Royal Statistical Society Series B, 2002, vol. 64, issue 4, 791-804

Abstract: Summary. The paper presents a general strategy for selecting the bandwidth of nonparametric regression estimators and specializes it to local linear regression smoothers. The procedure requires the sample to be divided into a training sample and a testing sample. Using the training sample we first compute a family of regression smoothers indexed by their bandwidths. Next we select the bandwidth by minimizing the empirical quadratic prediction error on the testing sample. The resulting bandwidth satisfies a finite sample oracle inequality which holds for all bounded regression functions. This permits asymptotically optimal estimation for nearly any regression function. The practical performance of the method is illustrated by a simulation study which shows good finite sample behaviour of our method compared with other bandwidth selection procedures.

Date: 2002
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