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Degrees-of-freedom tests for smoothing splines

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  • Eva Cantoni

Abstract

When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. The problem is addressed in the framework of a mixed-effects model, whose assumptions ensure that the resulting estimator is unbiased. A likelihood-ratio-type test statistic is proposed, and its exact distribution is derived. Tests of linearity and overall effect follow directly. We then extend this idea to additive models where it provides a more attractive alternative than multi-parameter optimisation, and where it gives exact distributional results that can be used in an analysis-of-deviance-type approach. Examples on real data and a simulation study of level and power complete the paper. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Eva Cantoni, 2002. "Degrees-of-freedom tests for smoothing splines," Biometrika, Biometrika Trust, vol. 89(2), pages 251-263, June.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:251-263
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    Cited by:

    1. Campos, Eduardo Lima & Cysne, Rubens Penha, 2017. "A time-varying fiscal reaction function for Brazil," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 795, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    2. Guizzardi, Andrea & Mariani, Marcello M. & Stacchini, Annalisa, 2022. "A temporal construal theory explanation of the price-quality relationship in online dynamic pricing," Journal of Business Research, Elsevier, vol. 146(C), pages 32-44.
    3. Avalos, Marta & Grandvalet, Yves & Ambroise, Christophe, 2007. "Parsimonious additive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2851-2870, March.
    4. Philip T. Reiss & R. Todd Ogden, 2009. "Smoothing parameter selection for a class of semiparametric linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 505-523, April.
    5. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 387-402, October.
    6. Fatemeh Hassanzadeh, 2021. "A smoothing spline model for multimodal and skewed circular responses: Applications in meteorology and oceanography," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    7. Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2372-2387, July.
    8. Yuanjia Wang & Huaihou Chen, 2012. "On Testing an Unspecified Function Through a Linear Mixed Effects Model with Multiple Variance Components," Biometrics, The International Biometric Society, vol. 68(4), pages 1113-1125, December.

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