Smoothing parameter selection in two frameworks for penalized splines
AbstractThere 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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Bibliographic InfoPaper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 85.
Date of creation: 02 Aug 2011
Date of revision: 18 Oct 2012
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Maximum likelihood; Mean squared error minimizer; Penalized splines; Smoothing splines;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-09 (All new papers)
- NEP-ECM-2011-08-09 (Econometrics)
- NEP-ETS-2011-08-09 (Econometric Time Series)
- NEP-ORE-2011-08-09 (Operations Research)
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