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Smoothing parameter selection in two frameworks for penalized splines


  • Tatyana Krivobokova

    Corresponding author
    1. Georg-August-Universität Göttingen, Germany
    • Address for correspondence: Tatyana Krivobokova, Courant Research Center “Poverty, equity and growth” and Institute for Mathematical Stochastics, Georg-August-Universität Göttingen, Wilhelm-Weber-Strasse 2, 37073 Göttingen, Germany. E-mail:

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There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated by minimizing criteria that approximate the average mean-squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. The asymptotic properties of both smoothing parameter estimators for penalized splines are studied and compared. A simulation study and a real data example illustrate the theoretical findings.