Statistics Papers

Document Type

Journal Article

Date of this Version

2009

Publication Source

The Annals of Statistics

Volume

37

Issue

2

Start Page

569

Last Page

595

DOI

10.1214/07-AOS538

Abstract

A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein’s unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the “dense” and “sparse” cases. The procedure is easy to implement. Numerical results show that it has superior finite sample performance in comparison to the other leading wavelet thresholding estimators.

Keywords

adaptivity, Besov body, block thresholding, James–Stein estimator, nonparametric regression, Stein’s unbiased risk estimate, wavelets

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Date Posted: 27 November 2017

This document has been peer reviewed.