On robust cross-validation for nonparametric smoothing

Oliver Morell (), Dennis Otto and Roland Fried

Computational Statistics, 2013, vol. 28, issue 4, 1617-1637

Abstract: An essential problem in nonparametric smoothing of noisy data is a proper choice of the bandwidth or window width, which depends on a smoothing parameter $$k$$ . One way to choose $$k$$ based on the data is leave-one-out-cross-validation. The selection of the cross-validation criterion is similarly important as the choice of the smoother. Especially, when outliers are present, robust cross-validation criteria are needed. So far little is known about the behaviour of robust cross-validated smoothers in the presence of discontinuities in the regression function. We combine different smoothing procedures based on local constant fits with each of several cross-validation criteria. These combinations are compared in a simulation study under a broad variety of data situations with outliers and abrupt jumps. There is not a single overall best cross-validation criterion, but we find Boente-cross-validation to perform well in case of large percentages of outliers and the Tukey-criterion in case of data situations with jumps, even if the data are contaminated with outliers. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Nonparametric regression; Jump-preserving smoothers; Outliers; Robust bandwidth selection; Structural breaks (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00180-012-0369-2

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