Statistics Papers

Document Type

Journal Article

Date of this Version

11-1-2002

Publication Source

Journal of Statistical Planning and Inference

Volume

108

Issue

1-2

Start Page

329

Last Page

349

DOI

10.1016/S0378-3758(02)00316-6

Abstract

We consider a block thresholding and vaguelet–wavelet approach to certain statistical linear inverse problems. Based on an oracle inequality, an adaptive block thresholding estimator for linear inverse problems is proposed and the asymptotic properties of the estimator are investigated. It is shown that the estimator enjoys a higher degree of adaptivity than the standard term-by-term thresholding methods; it attains the exact optimal rates of convergence over a range of Besov classes. The problem of estimating a derivative is considered in more detail as a test for the general estimation procedure. We show that the derivative estimator is spatially adaptive; it automatically adapts to the local smoothness of the function and attains the local adaptive minimax rate for estimating a derivative at a point.

Copyright/Permission Statement

© 2002. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

block thresholding, derivative, linear inverse problems, vaguelets, wavelets

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Date Posted: 27 November 2017

This document has been peer reviewed.