Locally optimal adaptive smoothing splines

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Smoothing splines are widely used for estimating an unknown function in the nonparametric regression. If data have large spatial variations, however, the standard smoothing splines (which adopt a global smoothing parameter lambda) perform poorly. Adaptive smoothing splines adopt a variable smoothing parameter lambda(x) (i.e. the smoothing parameter is a function of the design variable x) to adapt to varying roughness. In this paper, we derive an asymptotically optimal local penalty function for lambda(x) is an element of C-3 under suitable conditions. The derived locally optimal penalty function in turn is used for the development of a locally optimal adaptive smoothing spline estimator. In the numerical study, we show that our estimator performs very well using several simulated and real data sets.
Publisher
TAYLOR FRANCIS LTD
Issue Date
2012
Language
English
Article Type
Article
Keywords

BAYESIAN CONFIDENCE-INTERVALS; NONPARAMETRIC REGRESSION; CROSS-VALIDATION; NOISY DATA; KERNEL

Citation

JOURNAL OF NONPARAMETRIC STATISTICS, v.24, no.3, pp.665 - 680

ISSN
1048-5252
DOI
10.1080/10485252.2012.693610
URI
http://hdl.handle.net/10203/191186
Appears in Collection
IE-Journal Papers(저널논문)
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