{"id":"https://openalex.org/W2087028387","doi":"https://doi.org/10.1109/cig.2010.5592845","title":"On conditions for linearity of optimal estimation","display_name":"On conditions for linearity of optimal estimation","publication_year":2010,"publication_date":"2010-08-01","ids":{"openalex":"https://openalex.org/W2087028387","doi":"https://doi.org/10.1109/cig.2010.5592845","mag":"2087028387"},"language":"en","primary_location":{"id":"doi:10.1109/cig.2010.5592845","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cig.2010.5592845","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Information Theory Workshop","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012879525","display_name":"Emrah Akyol","orcid":"https://orcid.org/0000-0002-0663-1677"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Emrah Akyol","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California,\uc2a0Santa Barbara, CA, USA","Department of Electrical and Computer Engineering University of California at Santa Barbara, CA-93106"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California,\uc2a0Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering University of California at Santa Barbara, CA-93106","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017446531","display_name":"Kumar Viswanatha","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kumar Viswanatha","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California,\uc2a0Santa Barbara, CA, USA","Department of Electrical and Computer Engineering University of California at Santa Barbara, CA-93106"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California,\uc2a0Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering University of California at Santa Barbara, CA-93106","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026459097","display_name":"Kenneth Rose","orcid":"https://orcid.org/0000-0001-9463-2647"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth Rose","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California,\uc2a0Santa Barbara, CA, USA","Department of Electrical and Computer Engineering University of California at Santa Barbara, CA-93106"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California,\uc2a0Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering University of California at Santa Barbara, CA-93106","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012879525"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":2.1367,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88092382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9980999827384949,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9950000047683716,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7036982178688049},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.6369207501411438},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.6299880146980286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5154060125350952},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.5063737630844116},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4891858398914337},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.485475093126297},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.47968363761901855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4598053991794586},{"id":"https://openalex.org/keywords/noise-measurement","display_name":"Noise measurement","score":0.44315582513809204},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4046710133552551},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40214377641677856},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38232678174972534},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33887404203414917},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2379215955734253},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.10482892394065857},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08460038900375366},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08303412795066833},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.07815572619438171},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06953030824661255}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7036982178688049},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.6369207501411438},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.6299880146980286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5154060125350952},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.5063737630844116},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4891858398914337},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.485475093126297},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.47968363761901855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4598053991794586},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.44315582513809204},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4046710133552551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40214377641677856},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38232678174972534},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33887404203414917},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2379215955734253},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.10482892394065857},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08460038900375366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08303412795066833},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.07815572619438171},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06953030824661255},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cig.2010.5592845","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cig.2010.5592845","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Information Theory Workshop","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W577218644","https://openalex.org/W1525535255","https://openalex.org/W1534416612","https://openalex.org/W1634005169","https://openalex.org/W1967861999","https://openalex.org/W2056099894","https://openalex.org/W2059947873","https://openalex.org/W2085380472","https://openalex.org/W2086878253","https://openalex.org/W2111616148","https://openalex.org/W2112172398","https://openalex.org/W2141464269","https://openalex.org/W2148279974","https://openalex.org/W2170201775","https://openalex.org/W2188564768","https://openalex.org/W2293423476","https://openalex.org/W2610857016","https://openalex.org/W2911483801","https://openalex.org/W3150304496","https://openalex.org/W4206180546","https://openalex.org/W4206751862","https://openalex.org/W4300093168"],"related_works":["https://openalex.org/W2986378528","https://openalex.org/W3178345791","https://openalex.org/W1550854977","https://openalex.org/W2092661960","https://openalex.org/W4231055618","https://openalex.org/W2949211747","https://openalex.org/W3005742472","https://openalex.org/W2162441712","https://openalex.org/W2588855097","https://openalex.org/W1986743941"],"abstract_inverted_index":{"When":[0],"is":[1,6,95,109,114,125],"optimal":[2,39,76,123],"estimation":[3,27],"linear?":[4],"It":[5],"well-known":[7],"that,":[8,82],"in":[9,111],"the":[10,24,34,70,84,92,99,105,115,121],"case":[11],"of":[12,38,62],"a":[13,20,42,48,63],"Gaussian":[14,18,106],"source":[15,64,87,94],"contaminated":[16],"with":[17],"noise,":[19],"linear":[21,126],"estimator":[22,77,124],"minimizes":[23],"mean":[25],"square":[26],"error.":[28],"This":[29],"paper":[30],"analyzes":[31],"more":[32,128],"generally":[33],"conditions":[35,57],"for":[36,58,119],"linearity":[37],"estimators.":[40],"Given":[41],"noise":[43,52,85],"(or":[44,65],"source)":[45],"distribution,":[46],"and":[47,60,86],"specified":[49],"signal":[50],"to":[51,98],"ratio":[53],"(SNR),":[54],"we":[55,102],"derive":[56],"existence":[59],"uniqueness":[61],"noise)":[66],"distribution":[67],"that":[68,104,112],"renders":[69],"L":[71],"<sub":[72],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[73],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[74],"norm":[75],"linear.":[78],"We":[79],"then":[80,91],"show":[81],"if":[83],"variances":[88],"are":[89],"equal,":[90],"matching":[93],"distributed":[96],"identically":[97],"noise.":[100],"Moreover,":[101],"prove":[103],"source-channel":[107,117],"pair":[108,118],"unique":[110],"it":[113],"only":[116],"which":[120],"MSE":[122],"at":[127],"than":[129],"one":[130],"SNR":[131],"values.":[132]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":21},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}