Theory for penalised spline regression

Peter Hall; J. D. Opsomer

doi:10.1093/biomet/92.1.105

Theory for penalised spline regression

Peter Hall^*, J. D. Opsomer

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

66 Citations (Scopus)

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).

Original language	English
Pages (from-to)	105-118
Number of pages	14
Journal	Biometrika
Volume	92
Issue number	1
DOIs	https://doi.org/10.1093/biomet/92.1.105
Publication status	Published - Mar 2005

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AB - 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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Theory for penalised spline regression

Abstract

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