Theory for penalised spline regression
Date
2005
Authors
Hall, Peter
Opsomer, J D
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Publisher
Biometrika Trust
Abstract
Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to achieve the optimal nonparametric convergence rate established by Stone (1982).
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Keywords
Keywords: Nonparametric regression; White noise model
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Source
Biometrika
Type
Journal article
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2037-12-31
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