{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T18:37:02Z","timestamp":1780339022178,"version":"3.54.1"},"reference-count":16,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T00:00:00Z","timestamp":1745798400000},"content-version":"vor","delay-in-days":117,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,16]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>The three cardinal, statistically consistent families of nonparametric estimators for the power spectral density of a time series are the lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a finite sample, each can be subject to nonignorable bias. Astfalck et\u00a0al. (2024) developed a method that offers significant bias reduction for finite samples for Welch\u2019s estimator, which this article extends to the larger family of quadratic estimators, thus providing similar theory for bias correction of lag-window and multitaper estimators as well as combinations thereof. Importantly, this theory may be used in conjunction with any and all tapers and lag-sequences designed for bias reduction, and so should be seen as an extension to valuable work in these fields, rather than a supplanting methodology. The order of computation is larger than the $ {O}(n\\log n) $ which is typical in spectral analyses, but it is not insurmountable in practice. Simulation studies support the theory with comparisons across variations of quadratic estimators.<\/jats:p>","DOI":"10.1093\/biomet\/asaf033","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T12:22:16Z","timestamp":1745842936000},"source":"Crossref","is-referenced-by-count":3,"title":["Bias correction of quadratic spectral estimators"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8369-9384","authenticated-orcid":false,"given":"Lachlan C","family":"Astfalck","sequence":"first","affiliation":[{"name":"School of Physics, Mathematics & Computing, The University of Western Australia , 35 Stirling Highway , Crawley 6009,","place":["Australia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adam M","family":"Sykulski","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London , South Kensington, London SW7 2AZ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edward J","family":"Cripps","sequence":"additional","affiliation":[{"name":"School of Physics, Mathematics & Computing, The University of Western Australia , 35 Stirling Highway , Crawley 6009,","place":["Australia"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,4,28]]},"reference":[{"key":"2025081218573175200_asaf033-B1","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1093\/biomet\/asae033","article-title":"Debiasing Welch\u2019s method of spectral density estimation","volume":"111","author":"Astfalck","year":"2024","journal-title":"Biometrika"},{"key":"2025081218573175200_asaf033-B2","volume-title":"Time Series: Data Analysis and Theory","author":"Brillinger","year":"1975"},{"key":"2025081218573175200_asaf033-B3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1515\/crll.1910.138.22","article-title":"Lebesguessche Konstanten und divergente Fourierreihen","volume":"138","author":"Fej\u00e9r","year":"1910","journal-title":"J. reine angew. 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