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Biometrika Advance Access originally published online on January 30, 2009
Biometrika 2009 96(1):175-186; doi:10.1093/biomet/asn068
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© 2009 Biometrika Trust

Articles

Reducing variability of crossvalidation for smoothing-parameter choice

Peter Hall and Andrew P. Robinson

Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia halpstat{at}ms.unimelb.edu.au andrewpr{at}ms.unimelb.edu.au

Received for publication 1 August 2007. Revision received 1 June 2008.
  Abstract

One of the attractions of crossvalidation, as a tool for smoothing-parameter choice, is its applicability to a wide variety of estimator types and contexts. However, its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters, noting that this compromises the performance of the estimators in which those parameters are used. We show that the variability can be reduced simply, significantly and reliably by employing bootstrap aggregation or bagging. We establish that in theory, when bagging is implemented using an adaptively chosen resample size, the variability of crossvalidation can be reduced by an order of magnitude. However, it is arguably more attractive to use a simpler approach, based for example on half-sample bagging, which can reduce variability by approximately 50%.

Key Words: Bagging • Bandwidth • Bootstrap aggregation • Half-sampling • Kernel estimation • Nonparametric density estimation • Nonparametric regression • Statistical smoothing • Subsampling


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