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 rateestablished by Stone (1982). Copyright 2005, Oxford University Press.
Keywords
MathematicsSmoothing splineEstimatorSpline (mechanical)Nonparametric regressionPolynomial regressionConsistency (knowledge bases)Mean squared errorStatisticsMinimum-variance unbiased estimatorApplied mathematicsSmoothingThin plate splineRegression analysisSpline interpolation
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Publication Info
- Year
- 2005
- Type
- article
- Volume
- 92
- Issue
- 1
- Pages
- 105-118
- Citations
- 98
- Access
- Closed
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Cite This
Peter Hall,
Jean D. Opsomer
(2005).
Theory for penalised spline regression.
Biometrika
, 92
(1)
, 105-118.
https://doi.org/10.1093/biomet/92.1.105
Identifiers
- DOI
- 10.1093/biomet/92.1.105