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Spline Smoothing

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Definition: Spline smoothing is a particular nonparametric estimator of a function. Given a data set {Xi, Yi} it estimates values of Y for X's other than those in the sample. The process is to construct a function that balances the twin needs of (1) proximity to the actual sample points, (2) smoothness. So a 'roughness penalty' is defined. See Hardle's equation 3.4.1 near p. 56 for the 'cubic spline' which seems to be the most common.

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