A unified framework for spline estimators
AbstractThis article develops a unified framework to study the (asymptotic) properties of (periodic) spline based estimators, that is of regression, penalized and smoothing splines. We obtain an explicit form of the Demmler-Reinsch basis of general degree in terms of exponential splines and corresponding eigenvalues by applying Fourier techniques to periodic smoothers. This allows to derive exact expressions for the equivalent kernels of all spline estimators and get insights into the local and global asymptotic behavior of these estimators.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 130.
Date of creation: 20 Nov 2012
Date of revision:
Contact details of provider:
Postal: Platz der Goettinger Sieben 3; D-37073 Goettingen, GERMANY
Phone: +49 551 39 14066
Fax: + 49 551 39 14059
Web page: http://www.uni-goettingen.de/en/82144.html
B-splines; Equivalent kernels; Euler-Frobenius polynomials; Exponential splines; Demmler-Reinsch basis;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-06 (All new papers)
- NEP-ECM-2012-12-06 (Econometrics)
- NEP-ETS-2012-12-06 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503.
- Claeskens, Gerda & Krivobokova, Tatyana & Opsomer, Jean, 2009. "Asymptotic properties of penalized spline estimators," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/211475, Katholieke Universiteit Leuven.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
- Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dominik Noe).
If references are entirely missing, you can add them using this form.