Parametric modelling of thresholds across scales in wavelet regression

A Antoniadis, PZ Fryzlewicz

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)

Abstract

We propose a parametric wavelet thresholding procedure for estimation in the 'function plus independent, identically distributed Gaussian noise' model. To reflect the decreasing sparsity of wavelet coefficients from finer to coarser scales, our thresholds also decrease. They retain the noise-free reconstruction property while being lower than the universal threshold, and are jointly parameterised by a single scalar parameter. We show that our estimator achieves near-optimal risk rates for the usual range of Besov spaces. We propose a crossvalidation technique for choosing the parameter of our procedure. A simulation study demonstrates very good performance of our estimator compared to other state-of-the-art techniques. We discuss an extension to non-Gaussian noise.
Translated title of the contributionParametric modelling of thresholds across scales in wavelet regression
Original languageEnglish
Pages (from-to)465 - 471
Number of pages7
JournalBiometrika
Volume93 (2)
DOIs
Publication statusPublished - Jun 2006

Bibliographical note

Publisher: Oxford University Press
Other identifier: IDS Number 059VP

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