Journal article
Performance of robust GCV and modified GCV for spline smoothing
Scandinavian Journal of Statistics, Vol.39(1), pp.97-115
2012
Abstract
While it is a popular selection criterion for spline smoothing, generalized cross-validation (GCV) occasionally yields severely undersmoothed estimates. Two extensions of GCV called robust GCV (RGCV) and modified GCV have been proposed as more stable criteria. Each involves a parameter that must be chosen, but the only guidance has come from simulation results. We investigate the performance of the criteria analytically. In most studies, the mean square prediction error is the only loss function considered. Here, we use both the prediction error and a stronger Sobolev norm error, which provides a better measure of the quality of the estimate. A geometric approach is used to analyse the superior small-sample stability of RGCV compared to GCV. In addition, by deriving the asymptotic inefficiency for both the prediction error and the Sobolev error, we find intervals for the parameters of RGCV and modified GCV for which the criteria have optimal performance.
Details
- Title
- Performance of robust GCV and modified GCV for spline smoothing
- Authors/Creators
- M.A. Lukas (Author/Creator)F.R. de Hoog (Author/Creator)R.S. Anderssen (Author/Creator)
- Publication Details
- Scandinavian Journal of Statistics, Vol.39(1), pp.97-115
- Publisher
- Blackwell Publishing
- Identifiers
- 991005541343607891
- Copyright
- © 2011 Board of the Foundation of the Scandinavian Journal of Statistics
- Murdoch Affiliation
- School of Chemical and Mathematical Science
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.92 Statistical Methods
- 9.92.220 Robust Estimation
- Web Of Science research areas
- Statistics & Probability
- ESI research areas
- Mathematics