{"id":"https://openalex.org/W2127191392","doi":"https://doi.org/10.3390/e16020814","title":"A Note on the W-S Lower Bound of the MEE Estimation","display_name":"A Note on the W-S Lower Bound of the MEE Estimation","publication_year":2014,"publication_date":"2014-02-10","ids":{"openalex":"https://openalex.org/W2127191392","doi":"https://doi.org/10.3390/e16020814","mag":"2127191392"},"language":"en","primary_location":{"id":"doi:10.3390/e16020814","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16020814","pdf_url":"https://www.mdpi.com/1099-4300/16/2/814/pdf?version=1424785279","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/1099-4300/16/2/814/pdf?version=1424785279","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077852542","display_name":"Badong Chen","orcid":"https://orcid.org/0000-0003-1710-3818"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Badong Chen","raw_affiliation_strings":["Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China"],"raw_orcid":"https://orcid.org/0000-0003-1710-3818","affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066928904","display_name":"Guangmin Wang","orcid":"https://orcid.org/0000-0002-2350-4119"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangmin Wang","raw_affiliation_strings":["Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047405956","display_name":"Nanning Zheng","orcid":"https://orcid.org/0000-0003-1608-8257"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nanning Zheng","raw_affiliation_strings":["Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019504861","display_name":"Jos\u00e9 C. Pr\u0131\u0301ncipe","orcid":"https://orcid.org/0000-0002-3449-3531"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jose Principe","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1048913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"2","first_page":"814","last_page":"824"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.801112174987793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6894632577896118},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6049227714538574},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5714588165283203},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5438909530639648},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5023064613342285},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4641275405883789},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.45247238874435425},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.4417811930179596},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.43763667345046997},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4254189729690552},{"id":"https://openalex.org/keywords/entropy-estimation","display_name":"Entropy estimation","score":0.42012926936149597},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.41264572739601135},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.12087485194206238},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10264387726783752}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.801112174987793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894632577896118},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6049227714538574},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5714588165283203},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5438909530639648},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5023064613342285},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4641275405883789},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.45247238874435425},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4417811930179596},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.43763667345046997},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4254189729690552},{"id":"https://openalex.org/C95546049","wikidata":"https://www.wikidata.org/wiki/Q1345207","display_name":"Entropy estimation","level":3,"score":0.42012926936149597},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.41264572739601135},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.12087485194206238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10264387726783752},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/e16020814","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16020814","pdf_url":"https://www.mdpi.com/1099-4300/16/2/814/pdf?version=1424785279","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:0b90ef5a5d5c40c5b867639abab79ca3","is_oa":true,"landing_page_url":"https://doaj.org/article/0b90ef5a5d5c40c5b867639abab79ca3","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 16, Iss 2, Pp 814-824 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e16020814","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16020814","pdf_url":"https://www.mdpi.com/1099-4300/16/2/814/pdf?version=1424785279","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2127191392.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W9310736","https://openalex.org/W130992260","https://openalex.org/W565868953","https://openalex.org/W1965027861","https://openalex.org/W1972927542","https://openalex.org/W1978003802","https://openalex.org/W1990632278","https://openalex.org/W1995852180","https://openalex.org/W1996773351","https://openalex.org/W2011976556","https://openalex.org/W2041435955","https://openalex.org/W2042558795","https://openalex.org/W2045551057","https://openalex.org/W2048449370","https://openalex.org/W2068708092","https://openalex.org/W2086878253","https://openalex.org/W2087454975","https://openalex.org/W2097521973","https://openalex.org/W2107154726","https://openalex.org/W2124572691","https://openalex.org/W2132637751","https://openalex.org/W2139272549","https://openalex.org/W2148319325","https://openalex.org/W2165898564","https://openalex.org/W2395855665","https://openalex.org/W2483813931","https://openalex.org/W4230367971","https://openalex.org/W6605329539","https://openalex.org/W6711939863"],"related_works":["https://openalex.org/W2053566994","https://openalex.org/W202303397","https://openalex.org/W2279821256","https://openalex.org/W588585258","https://openalex.org/W2147544021","https://openalex.org/W415812316","https://openalex.org/W1988884164","https://openalex.org/W4287550078","https://openalex.org/W1601475477","https://openalex.org/W3114522307"],"abstract_inverted_index":{"The":[0],"minimum":[1,41],"error":[2,31,44],"entropy":[3,27,72],"(MEE)":[4],"estimation":[5,10,30,35,46],"is":[6,32,52,67,95,132],"concerned":[7],"with":[8],"the":[9,26,29,39,58,62,70,74,85,107,115,122,128],"of":[11,28,73,114,124],"a":[12,88],"certain":[13],"random":[14,21],"variable":[15,22,76],"(unknown":[16],"variable)":[17],"based":[18],"on":[19,57,98],"another":[20],"(observation),":[23],"so":[24],"that":[25],"minimized.":[33],"This":[34],"method":[36],"may":[37],"outperform":[38],"well-known":[40],"mean":[42],"square":[43],"(MMSE)":[45],"especially":[47],"for":[48,87],"non-Gaussian":[49],"situations.":[50],"There":[51],"an":[53],"important":[54],"performance":[55,100],"bound":[56,118,131],"MEE":[59],"estimation,":[60],"namely":[61],"W-S":[63,108,116,129],"lower":[64,109,117,130],"bound,":[65],"which":[66],"computed":[68],"as":[69],"conditional":[71],"unknown":[75],"given":[77],"observation.":[78],"Though":[79],"it":[80],"has":[81],"been":[82],"known":[83],"in":[84],"literature":[86],"considerable":[89],"time,":[90],"up":[91],"to":[92],"now":[93],"there":[94],"little":[96],"study":[97],"this":[99,103],"bound.":[101,110],"In":[102],"paper,":[104],"we":[105],"reexamine":[106],"Some":[111],"basic":[112],"properties":[113],"are":[119],"presented,":[120],"and":[121],"characterization":[123],"Gaussian":[125],"distribution":[126],"using":[127],"investigated.":[133]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}