Posterior probability intervals for wavelet thresholding

S Barber, GP Nason, BW Silverman

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

16 Citations (Scopus)

Abstract

We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale. Hence, a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any given data set. Johnson transformations then yield the credible intervals themselves. Simulations show that these intervals have good coverage rates, even when the underlying function is inhomogeneous, where standard methods fail. In the case where the curve is smooth, the performance of our intervals remains competitive with established nonparametric regression methods.
Translated title of the contributionPosterior probability intervals for wavelet thresholding
Original languageEnglish
Pages (from-to)189 - 205
Number of pages17
JournalJournal of the Royal Statistical Society Series B - Statistical Methodology
Volume64 (2)
DOIs
Publication statusPublished - May 2002

Bibliographical note

Publisher: Blackwell Publ Ltd

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