{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T03:12:32Z","timestamp":1761016352368,"version":"3.37.3"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2004,10,13]],"date-time":"2004-10-13T00:00:00Z","timestamp":1097625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["AF\/001664"],"award-info":[{"award-number":["AF\/001664"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2004.b5604.x","type":"journal-article","created":{"date-parts":[[2004,10,13]],"date-time":"2004-10-13T08:22:05Z","timestamp":1097655725000},"page":"927-939","source":"Crossref","is-referenced-by-count":33,"title":["Real Nonparametric Regression Using Complex Wavelets"],"prefix":"10.1093","volume":"66","author":[{"given":"Stuart","family":"Barber","sequence":"first","affiliation":[{"name":"University of Bristol , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guy P.","family":"Nason","sequence":"additional","affiliation":[{"name":"University of Bristol , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2004,10,13]]},"reference":[{"key":"2023040701583382100_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/1467-9884.00216","article-title":"Wavelet analysis and its statistical applications","volume":"49","author":"Abramovich","year":"2000","journal-title":"Statistician"},{"key":"2023040701583382100_","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/0167-9473(96)00003-5","article-title":"Adaptive thresholding of wavelet coefficients","volume":"22","author":"Abramovich","year":"1996","journal-title":"Comput. 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