Skip Navigation

Biometrika 2009 96(3):529-544; doi:10.1093/biomet/asp035
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Claeskens, G.
Right arrow Articles by Opsomer, J. D.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 Biometrika Trust

Article

Asymptotic properties of penalized spline estimators

Gerda Claeskens

Katholieke Universiteit Leuven, Operations Research & Business Statistics and Leuven Statistics Research Center, Naamsestraat 69, B-3000 Leuven, Belgium gerda.claeskens{at}econ.kuleuven.be

Tatyana Krivobokova

Georg-August-Universität Göttingen, CRC Poverty, Equity and Growth, Platz der Göttinger Sieben 3, D-37073 Göttingen, Germany tatyana.krivobokova{at}wiwi.uni-goettingen.de

Jean D. Opsomer

Colorado State University Department of Statistics, Fort Collins, Colorado 80523, U.S.A. jopsomer{at}stat.colostate.edu

Received for publication 1 September 2008. Revision received 1 December 2008.
  Abstract

We study the class of penalized spline estimators, which enjoy similarities to both regression splines, without penalty and with fewer knots than data points, and smoothing splines, with knots equal to the data points and a penalty controlling the roughness of the fit. Depending on the number of knots, sample size and penalty, we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of smoothing splines, with a clear breakpoint distinguishing the cases. We prove that using fewer knots results in better asymptotic rates than when using a large number of knots. We obtain expressions for bias and variance and asymptotic rates for the number of knots and penalty parameter.

Key Words: Mean squared error • Nonparametric regression • Penalty • Regression spline • Smoothing spline


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.