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Biometrika 2006 93(1):113-125; doi:10.1093/biomet/93.1.113
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© 2006 Biometrika Trust

Spatially adaptive smoothing splines

Alexandre Pintore1, Paul Speckman2 and Chris C. Holmes3

1 Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, U.K. pintore{at}stats.ox.ac.uk, 2 Department of Statistics, University of Missouri, Columbia, Missouri 65211-6100, U.S.A. speckman{at}stats.missouri.edu, 3 Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, U.K. cholmes{at}stats.ox.ac.uk

We use a reproducing kernel Hilbert space representation to derive the smoothing spline solution when the smoothness penalty is a function {lambda}(t) of the design space t, thereby allowing the model to adapt to various degrees of smoothness in the structure of the data. We propose a convenient form for the smoothness penalty function and discuss computational algorithms for automatic curve fitting using a generalised crossvalidation measure.

Key Words: Curve fitting; Generalised crossvalidation; Smoothing spline; Spatial adaption; Spline

Received July 2003. Revised July 2005.


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