{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:23:07Z","timestamp":1770981787446,"version":"3.50.1"},"reference-count":12,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[1976,1,1]],"date-time":"1976-01-01T00:00:00Z","timestamp":189302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1976,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>This paper is concerned with the estimation of the parameters in a simple open-loop differential equation model. We suggest first some frequency-domain \u201cnarrow-band\u201d and \u201cbroad-band\u201d estimators that are based on the assumption that the observable input variable has no spectral mass beyond Nyquist frequency. We study the asymptotic biases of these estimators under the contradictory hypothesis that the spectral density of the input is a rational function of frequency. On considering the limiting situation of the sampling interval converging to zero, we derive relatively simple multiplicative correction factors that can be applied to the original estimates, with the objective of reducing the bias.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1976.tb01584.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:24:47Z","timestamp":1544163887000},"page":"180-188","source":"Crossref","is-referenced-by-count":3,"title":["The Aliasing Problem in Differential Equation Estimation"],"prefix":"10.1093","volume":"38","author":[{"given":"P. M.","family":"Robinson","sequence":"first","affiliation":[{"name":"Harvard University and University of California , Berkeley"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920480862200_rssb01584-cit-0001","doi-asserted-by":"crossref","first-page":"27","DOI":"10.2307\/2983611","article-title":"On the theoretical specification of sampling properties of autocorrelated time series","volume":"8","author":"Bartlett","year":"1946","journal-title":"J. R. Statist. Soc. Suppl."},{"key":"2024090920480862200_rssb01584-cit-0002","first-page":"273","article-title":"Efficient fitting of linear models for continuous stationary time series from discrete data","volume":"38","author":"Durbin","year":"1961","journal-title":"Bull. Int. Statist. 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B"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1976.tb01584.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/38\/2\/180\/49096526\/jrsssb_38_2_180.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/38\/2\/180\/49096526\/jrsssb_38_2_180.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T21:13:36Z","timestamp":1725916416000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/38\/2\/180\/7027363"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1976,1,1]]},"references-count":12,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1976,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1976.tb01584.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1976,1]]},"published":{"date-parts":[[1976,1,1]]}}}