{"id":"https://openalex.org/W2108571308","doi":"https://doi.org/10.3390/e15061999","title":"Bias Adjustment for a Nonparametric Entropy Estimator","display_name":"Bias Adjustment for a Nonparametric Entropy Estimator","publication_year":2013,"publication_date":"2013-05-23","ids":{"openalex":"https://openalex.org/W2108571308","doi":"https://doi.org/10.3390/e15061999","mag":"2108571308"},"language":"en","primary_location":{"id":"doi:10.3390/e15061999","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15061999","pdf_url":"https://www.mdpi.com/1099-4300/15/6/1999/pdf?version=1424785019","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/15/6/1999/pdf?version=1424785019","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100764276","display_name":"Zhiyi Zhang","orcid":"https://orcid.org/0000-0003-1175-1259"},"institutions":[{"id":"https://openalex.org/I102149020","display_name":"University of North Carolina at Charlotte","ror":"https://ror.org/04dawnj30","country_code":"US","type":"education","lineage":["https://openalex.org/I102149020"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhiyi Zhang","raw_affiliation_strings":["Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA","institution_ids":["https://openalex.org/I102149020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049418599","display_name":"Michael Grabchak","orcid":"https://orcid.org/0000-0003-2547-0167"},"institutions":[{"id":"https://openalex.org/I102149020","display_name":"University of North Carolina at Charlotte","ror":"https://ror.org/04dawnj30","country_code":"US","type":"education","lineage":["https://openalex.org/I102149020"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Grabchak","raw_affiliation_strings":["Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA","institution_ids":["https://openalex.org/I102149020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100764276"],"corresponding_institution_ids":["https://openalex.org/I102149020"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4979,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.83226197,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"6","first_page":"1999","last_page":"2011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.983299970626831,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.983299970626831,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9732000231742859,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8152643442153931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6793278455734253},{"id":"https://openalex.org/keywords/consistent-estimator","display_name":"Consistent estimator","score":0.5572651624679565},{"id":"https://openalex.org/keywords/invariant-estimator","display_name":"Invariant estimator","score":0.5379821062088013},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.5245431065559387},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.5095951557159424},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49912166595458984},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.48285943269729614},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46017566323280334},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.44969800114631653},{"id":"https://openalex.org/keywords/entropy-estimation","display_name":"Entropy estimation","score":0.4236499071121216},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.4143886864185333},{"id":"https://openalex.org/keywords/minimax-estimator","display_name":"Minimax estimator","score":0.4105771780014038},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10095325112342834},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.05332744121551514}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8152643442153931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6793278455734253},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.5572651624679565},{"id":"https://openalex.org/C38689907","wikidata":"https://www.wikidata.org/wiki/Q6059509","display_name":"Invariant estimator","level":5,"score":0.5379821062088013},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.5245431065559387},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5095951557159424},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49912166595458984},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.48285943269729614},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46017566323280334},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.44969800114631653},{"id":"https://openalex.org/C95546049","wikidata":"https://www.wikidata.org/wiki/Q1345207","display_name":"Entropy estimation","level":3,"score":0.4236499071121216},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4143886864185333},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.4105771780014038},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10095325112342834},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.05332744121551514},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/e15061999","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15061999","pdf_url":"https://www.mdpi.com/1099-4300/15/6/1999/pdf?version=1424785019","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8310c22aa0a04537af30f2ac01d32dd1","is_oa":true,"landing_page_url":"https://doaj.org/article/8310c22aa0a04537af30f2ac01d32dd1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 15, Iss 6, Pp 1999-2011 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e15061999","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15061999","pdf_url":"https://www.mdpi.com/1099-4300/15/6/1999/pdf?version=1424785019","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G559637779","display_name":"Estimation of Discrete Probablility Distribution with a Pareto Tail","funder_award_id":"1004769","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108571308.pdf","grobid_xml":"https://content.openalex.org/works/W2108571308.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1971405816","https://openalex.org/W1980179247","https://openalex.org/W1995875735","https://openalex.org/W2008551287","https://openalex.org/W2017856804","https://openalex.org/W2032440662","https://openalex.org/W2039728913","https://openalex.org/W2047701135","https://openalex.org/W2062829699","https://openalex.org/W2079473986","https://openalex.org/W2082092506","https://openalex.org/W2097173970","https://openalex.org/W2101985079","https://openalex.org/W2109584604","https://openalex.org/W2114771311","https://openalex.org/W2141753389","https://openalex.org/W2999905431","https://openalex.org/W3104209297","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2036696807","https://openalex.org/W2375720303","https://openalex.org/W2160772450","https://openalex.org/W2359371365","https://openalex.org/W2462295642","https://openalex.org/W2350206592","https://openalex.org/W2731761402","https://openalex.org/W2180134060","https://openalex.org/W2475279666","https://openalex.org/W4387582659"],"abstract_inverted_index":{"Zhang":[0],"in":[1],"2012":[2],"introduced":[3],"a":[4,22,37,51],"nonparametric":[5],"estimator":[6,39,49],"of":[7,28,40],"Shannon\u2019s":[8],"entropy,":[9],"whose":[10],"bias":[11,27,47,54],"decays":[12],"exponentially":[13],"fast":[14],"when":[15,66,72],"the":[16,26,64,67],"alphabet":[17,68],"is":[18,69,74],"finite.":[19],"We":[20,31,61],"propose":[21],"methodology":[23],"to":[24,35],"estimate":[25],"this":[29,46],"estimator.":[30],"then":[32],"use":[33],"it":[34,73],"construct":[36],"new":[38],"entropy.":[41],"Simulation":[42],"results":[43],"suggest":[44],"that":[45],"adjusted":[48],"has":[50],"significantly":[52],"lower":[53],"than":[55],"many":[56],"other":[57],"commonly":[58],"used":[59],"estimators.":[60],"consider":[62],"both":[63],"case":[65],"finite":[70],"and":[71],"countably":[75],"infinite.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
