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Bandwidth selection for local linear regression smoothers

Author

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  • Nicolas W. Hengartner
  • Marten H. Wegkamp
  • Eric Matzner‐Løber

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.

Suggested Citation

  • Nicolas W. Hengartner & Marten H. Wegkamp & Eric Matzner‐Løber, 2002. "Bandwidth selection for local linear regression smoothers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 791-804, October.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:4:p:791-804
    DOI: 10.1111/1467-9868.00361
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    Cited by:

    1. Reinowski, Eva, 2004. "Mikroökonometrische Evaluation und das Selektionsproblem – Ein anwendungsorientierter Überblick über nichtparametrische Lösungsverfahren –," IWH Discussion Papers 200/2004, Halle Institute for Economic Research (IWH).
    2. Zheng, Qi & Kulasekera, K.B. & Gallagher, Colin, 2010. "Local adaptive smoothing in kernel regression estimation," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 540-547, April.

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