Skip Navigation

Biometrika 1996 83(4):727-745; doi:10.1093/biomet/83.4.727
© 1996 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 BRUCE, A. G.
Right arrow Articles by GAO, H.-Y.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Understanding WaveShrink: Variance and bias estimation

ANDREW G. BRUCE and HONG-YE GAO

Data Analysis Products Division, MathSoft, Inc. 1700 Westlake Avenue N, Suite 500, Seattle, Washington 98109-9891, U.S.A.

Donoho & Johnstone's WaveShrink procedure has proved valuable for function estimation and nonparametric regression. WaveShrink is based on the principle of shrinking wavelet coefficients towards zero to remove noise. WaveShrink has very broad asymptotic near-optimality properties and achieves the optimal risk to within a factor of log n. In this paper, we derive computationally efficient formulae for computing the exact bias, variance and L2 risk of WaveShrink estimates in finite sample situations. We use these formulae to understand the behaviour of WaveShrink estimators, construct approximate confidence intervals and bias estimates for WaveShrink and compute ideal thresholds for a given function. We show that hard shrinkage has smaller bias but larger variance than soft shrinkage, and that significantly smaller thresholds should be used for soft shrinkage. We also compute minimax thresholds for WaveShrink estimators and demonstrate that the minimax thresholds can nearly achieve the ideal rank for a range of functions.

Key Words: Bias and variance estimation • Confidence interval • Function estimation • Hard shrinkage • Minimax estimation • Nonparametric regression • Soft Shrinkage • Threshold selection • Wavelet transform • WaveShrink


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.