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Smoothing parameter selection in two frameworks for penalized splines

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  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

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    Abstract

    There are two popular smoothing parameter selection methods for spline smoothing. First, criteria that approximate the average mean squared error of the estimator (e.g. generalized cross validation) are widely used. Alternatively, the maximum likelihood paradigm can be employed under the assumption that the underlying function to be estimated is a realization of some stochastic process. In this article the asymptotic properties of both smoothing parameter estimators are studied and compared in the frequentist and stochastic framework for penalized spline smoothing. Consistency and asymptotic normality of the estimators are proved and small sample properties are discussed. A simulation study and a real data example illustrate the theoretical fi ndings.

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    File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_85.pdf
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    Bibliographic Info

    Paper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 85.

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    Date of creation: 02 Aug 2011
    Date of revision: 18 Oct 2012
    Handle: RePEc:got:gotcrc:085

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    Web page: http://www.uni-goettingen.de/en/82144.html

    Related research

    Keywords: Maximum likelihood; Mean squared error minimizer; Penalized splines; Smoothing splines;

    This paper has been announced in the following NEP Reports:

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, April.
    2. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 243-247, December.
    3. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
    5. 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.
    6. Kou S.C. & Efron B., 2002. "Smoothers and the Cp, Generalized Maximum Likelihood, and Extended Exponential Criteria: A Geometric Approach," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 766-782, September.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, April.
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    Cited by:
    1. Luis Francisco Rosales & Tatyana Krivobokova, 2012. "Instant Trend-Seasonal Decomposition of Time Series with Splines," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 131, Courant Research Centre PEG.

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