Skip Navigation


Biometrika Advance Access originally published online on October 29, 2008
Biometrika 2008 95(4):907-917; doi:10.1093/biomet/asn041
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
95/4/907    most recent
asn041v1
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 Zhu, Z.
Right arrow Articles by He, X.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 Biometrika Trust

Articles

On the asymptotics of marginal regression splines with longitudinal data

Zhongyi Zhu

Department of Statistics, Fudan University, Shanghai 200433, China zhuzy{at}fudan.edu.cn

Wing K. Fung

Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China wingfung{at}hku.hk

Xuming He

Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, Illinois 61820, U.S.A. x-he{at}uiuc.edu

Received for publication 1 March 2007. Revision received 1 April 2008.
  Abstract

There have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within-cluster correlation when nonparametric regression models are used on longitudinal or cluster data. In particular, methods based on smoothing splines and local polynomial kernels exhibit different behaviour. We show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an interesting property: the asymptotic bias of the estimator does not depend on the working correlation matrix, but the asymptotic variance, and therefore the mean squared error, is minimized when the true correlation structure is specified. This property of the asymptotic bias distinguishes regression splines from smoothing splines.

Key Words: Asymptotic bias • B-spline • Generalized estimating equation • Generalized linear model • Least squares • Longitudinal data


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.