Theory for penalised spline regression

Peter Hall*, J. D. Opsomer

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    66 Citations (Scopus)


    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 languageEnglish
    Pages (from-to)105-118
    Number of pages14
    Issue number1
    Publication statusPublished - Mar 2005


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