Smoothing parameter selection in two frameworks for penalized splines
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.
|Date of creation:||02 Aug 2011|
|Date of revision:||18 Oct 2012|
|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
References listed on IDEAS
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.:
- 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.
- Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
- 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.
- Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
When requesting a correction, please mention this item's handle: RePEc:got:gotcrc:085. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dominik Noe)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.