{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T21:41:58Z","timestamp":1790890918524,"version":"4.1.0"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T00:00:00Z","timestamp":1719878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Welch\u2019s method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite-length time series, while the variance of the estimator decreases as the number of segments increases, the magnitude of the estimator\u2019s bias increases: a bias-variance trade-off ensues when setting the segment number. We address this issue by providing a novel method for debiasing Welch\u2019s method that maintains the computational complexity and asymptotic consistency, and leads to improved finite-sample performance. Theoretical results are given for fourth-order stationary processes with finite fourth-order moments and an absolutely convergent fourth-order cumulant function. The significant bias reduction is demonstrated with numerical simulation and an application to real-world data. Our estimator also permits irregular spacing over frequency and we demonstrate how this may be employed for signal compression and further variance reduction. The code accompanying this work is available in R and python.<\/jats:p>","DOI":"10.1093\/biomet\/asae033","type":"journal-article","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:14:50Z","timestamp":1719792890000},"page":"1313-1329","source":"Crossref","is-referenced-by-count":33,"title":["Debiasing Welch\u2019s method for spectral density estimation"],"prefix":"10.1093","volume":"111","author":[{"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":[[2024,7,2]]},"reference":[{"key":"2024112207521102100_asae033-B1","volume-title":"The Statistical Analysis of Time Series","author":"Anderson","year":"1971"},{"key":"2024112207521102100_asae033-B2","doi-asserted-by":"publisher","DOI":"10.1029\/2008GL037030","article-title":"Observation of swell dissipation across oceans","volume":"36","author":"Ardhuin","year":"2009","journal-title":"Geophys. 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