Skip Navigation

Biometrika 1988 75(2):189-199; doi:10.1093/biomet/75.2.189
© 1988 by Biometrika Trust
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 BUCKLEY, M. J.
Right arrow Articles by SILVERMAN, B. W.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

The estimation of residual variance in nonparametric regression

M. J. BUCKLEY, G. K. EAGLESON and B. W. SILVERMAN

CSIRO Division of Mathematics and Statistics Lindfield, N.S.W. 2070, Australia
School of Mathematical Sciences, University of Bath Bath BA2 7AY, U.K.

A wide class of estimators of the residual variance in nonparametric regression is considered, namely those that are quadratic in the data, unbiased for linear regression, and always nonnegative. The minimax mean squared error estimator over a natural class of regression functions is derived. This optimal estimator has an interesting structure and is closely related to a minimax estimator of the regression curve itself.

Key Words: Curve estimation • Minimax • Roughness penalty • 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.