Skip Navigation

Biometrika 2005 92(1):105-118; doi:10.1093/biomet/92.1.105
This Article
Right arrow Full Text (PDF)
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 Hall, P.
Right arrow Articles by Opsomer, J. D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2005 Biometrika Trust

Theory for penalised spline regression

Peter Hall1 and J. D. Opsomer2

1 Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia peter.hall{at}anu.edu.au, 2 Department of Statistics, Iowa State University, Ames, Iowa 50011, U.S.A. jopsomer{at}iastate.edu

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to achieve the optimal nonparametric convergence rateestablished by Stone (1982).

Key Words: Nonparametric regression; White noise model

Received October 2003. Revised May 2004.


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


This article has been cited by other articles:


Home page
 BiometrikaHome page
G. Claeskens, T. Krivobokova, and J. D. Opsomer
Asymptotic properties of penalized spline estimators
Biometrika, September 1, 2009; 96(3): 529 - 544.
[Abstract] [PDF]

Home page
 BiometrikaHome page
Y. Li and D. Ruppert
On the asymptotics of penalized splines
Biometrika, June 1, 2008; 95(2): 415 - 436.
[Abstract] [PDF]


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.