Real nonparametric regression using complex wavelets

S Barber, GP Nason

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

39 Citations (Scopus)


Wavelet shrinkage is an effective nonparametric regression technique, especially when the underlying curve has irregular features such as spikes or discontinuities. The basic idea is simple: take the discrete wavelet transform of data consisting of a signal corrupted by noise; shrink or remove the wavelet coefficients to remove the noise; then invert the discrete wavelet transform to form an estimate of the true underlying curve. Various researchers have proposed increasingly sophisticated methods of doing this by using real-valued wavelets. Complex-valued wavelets exist but are rarely used. We propose two new complex-valued wavelet shrinkage techniques: one based on multiwavelet style shrinkage and the other using Bayesian methods. Extensive simulations show that our methods almost always give significantly more accurate estimates than methods based on real-valued wavelets. Further, our multiwavelet style shrinkage method is both simpler and dramatically faster than its competitors. To understand the excellent performance of this method we present a new risk bound on its hard thresholded coefficients.
Translated title of the contributionReal nonparametric regression using complex wavelets
Original languageEnglish
Pages (from-to)927 - 939
Number of pages13
JournalJournal of the Royal Statistical Society: Series B, Statistical Methodology
Volume66 (4)
Publication statusPublished - Nov 2004

Bibliographical note

Publisher: Blackwell
Other identifier: IDS Number: 861UU


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