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Practical use of robust GCV and modified GCV for spline smoothing

Lukas, M.A., de Hoog, F.R. and Anderssen, R.S. (2015) Practical use of robust GCV and modified GCV for spline smoothing. Computational Statistics, 31 (1). pp. 269-289.

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Generalized cross-validation (GCV) is a popular parameter selection criterion for spline smoothing of noisy data, but it sometimes yields a severely undersmoothed estimate, especially if the sample size is small. Robust GCV (RGCV) and modified GCV are stable extensions of GCV, with the degree of stabilization depending on a parameter (Formula presented.) for RGCV and on a parameter (Formula presented.) for modified GCV. While there are favorable asymptotic results about the performance of RGCV and modified GCV, little is known for finite samples. In a large simulation study with cubic splines, we investigate the behavior of the optimal values of (Formula presented.) and (Formula presented.), and identify simple practical rules to choose them that are close to optimal. With these rules, both RGCV and modified GCV perform significantly better than GCV. The performance is defined in terms of the Sobolev error, which is shown by example to be more consistent with a visual assessment of the fit than the prediction error (average squared error). The results are consistent with known asymptotic results.

Publication Type: Journal Article
Murdoch Affiliation: School of Engineering and Information Technology
Publisher: Springer Verlag
Copyright: © 2015 Springer-Verlag Berlin Heidelberg
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