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Spline smoothing with model-based penalties

1997; Springer Science+Business Media; Volume: 29; Issue: 1 Linguagem: Inglês

10.3758/bf03200573

1532-5970

J. O. Ramsay, Nancy Heckman, B. W. Silverman,

Image and Signal Denoising Methods

Nonparametric regression techniques, which estimate functions directly from noisy data rather than relying on specific parametric models, now play a central role in statistical analysis. We can improve the efficiency and other aspects of a nonparametric curve estimate by using prior knowledge about general features of the curve in the smoothing process. Spline smoothing is extended in this paper to express this prior knowledge in the form of a linear differential operator that annihilates a specified parametric model for the data. Roughness in the fitted function is defined in terms of the integrated square of this operator applied to the fitted function. A fastO(n) algorithm is outlined for this smart smoothing process. Illustrations are provided of where this technique proves useful.