Adaptive Wavelet Estimation: A Block Thresholding and Oracle Inequality Approach

Loading...
Thumbnail Image
Penn collection
Statistics Papers
Degree type
Discipline
Subject
adaptivity
Besov space
block thresholding
James-Stein estimator
nonparametric regression
oracle inequality
spatial adaptivity
wavelets
Statistics and Probability
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Cai, T. Tony
Contributor
Abstract

We study wavelet function estimation via the approach of block thresholding and ideal adaptation with oracle. Oracle inequalities are derived and serve as guides for the selection of smoothing parameters. Based on an oracle inequality and motivated by the data compression and localization properties of wavelets, an adaptive wavelet estimator for nonparametric regression is proposed and the optimality of the procedure is investigated. We show that the estimator achieves simultaneously three objectives: adaptivity, spatial adaptivity and computational efficiency. Specifically, it is proved that the estimator attains the exact optimal rates of convergence over a range of Besov classes and the estimator achieves adaptive local minimax rate for estimating functions at a point. The estimator is easy to implement, at the computational cost of O(n). Simulation shows that the estimator has excellent numerical performance relative to more traditional wavelet estimators.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
1999
Journal title
Annals of Statistics
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Recommended citation
Collection