{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T05:18:05Z","timestamp":1774070285577,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2013,5,23]],"date-time":"2013-05-23T00:00:00Z","timestamp":1369267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Zhang in 2012 introduced a nonparametric estimator of Shannon\u2019s entropy, whose bias decays exponentially fast when the alphabet is finite. We propose a methodology to estimate the bias of this estimator. We then use it to construct a new estimator of entropy. Simulation results suggest that this bias adjusted estimator has a significantly lower bias than many other commonly used estimators. We consider both the case when the alphabet is finite and when it is countably infinite.<\/jats:p>","DOI":"10.3390\/e15061999","type":"journal-article","created":{"date-parts":[[2013,5,23]],"date-time":"2013-05-23T12:56:11Z","timestamp":1369313771000},"page":"1999-2011","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Bias Adjustment for a Nonparametric Entropy Estimator"],"prefix":"10.3390","volume":"15","author":[{"given":"Zhiyi","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Grabchak","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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