{"id":"https://openalex.org/W2123226256","doi":"https://doi.org/10.1109/tsp.2009.2022897","title":"Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory","display_name":"Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory","publication_year":2009,"publication_date":"2009-09-16","ids":{"openalex":"https://openalex.org/W2123226256","doi":"https://doi.org/10.1109/tsp.2009.2022897","mag":"2123226256"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2022897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2022897","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-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/A5045878067","display_name":"Shira Kritchman","orcid":null},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"S. Kritchman","raw_affiliation_strings":["Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel","Dept. of Comput. Sci. & Applied Math., Weizmann Inst. of Sci., Rehovot, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Applied Math., Weizmann Inst. of Sci., Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034942163","display_name":"Boaz Nadler","orcid":"https://orcid.org/0000-0002-9777-4576"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"B. Nadler","raw_affiliation_strings":["Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel","Dept. of Comput. Sci. & Applied Math., Weizmann Inst. of Sci., Rehovot, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Applied Math., Weizmann Inst. of Sci., Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I53964585"],"apc_list":null,"apc_paid":null,"fwci":13.3408,"has_fulltext":false,"cited_by_count":307,"citation_normalized_percentile":{"value":0.992,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"57","issue":"10","first_page":"3930","last_page":"3941"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9799000024795532,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/random-matrix","display_name":"Random matrix","score":0.7222496867179871},{"id":"https://openalex.org/keywords/detection-theory","display_name":"Detection theory","score":0.7070351839065552},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.6651372313499451},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6171298623085022},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.601250171661377},{"id":"https://openalex.org/keywords/minimum-description-length","display_name":"Minimum description length","score":0.5819292068481445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5484930276870728},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5362996459007263},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5355232954025269},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47529613971710205},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.47239017486572266},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4327976703643799},{"id":"https://openalex.org/keywords/statistical-signal-processing","display_name":"Statistical signal processing","score":0.4234829545021057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3843582272529602},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.246890127658844},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11659061908721924},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08954355120658875}],"concepts":[{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.7222496867179871},{"id":"https://openalex.org/C137270730","wikidata":"https://www.wikidata.org/wiki/Q120811","display_name":"Detection theory","level":3,"score":0.7070351839065552},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.6651372313499451},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6171298623085022},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.601250171661377},{"id":"https://openalex.org/C87465248","wikidata":"https://www.wikidata.org/wiki/Q1417790","display_name":"Minimum description length","level":2,"score":0.5819292068481445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5484930276870728},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5362996459007263},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5355232954025269},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47529613971710205},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.47239017486572266},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4327976703643799},{"id":"https://openalex.org/C105125183","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Statistical signal processing","level":4,"score":0.4234829545021057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3843582272529602},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.246890127658844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11659061908721924},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08954355120658875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2009.2022897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2022897","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W93530381","https://openalex.org/W641242542","https://openalex.org/W1500470240","https://openalex.org/W1520752838","https://openalex.org/W1546851689","https://openalex.org/W1602800129","https://openalex.org/W1634806857","https://openalex.org/W1814500939","https://openalex.org/W1964492749","https://openalex.org/W1972026932","https://openalex.org/W1972334750","https://openalex.org/W1981745143","https://openalex.org/W1993405207","https://openalex.org/W1996340537","https://openalex.org/W2005263452","https://openalex.org/W2014999546","https://openalex.org/W2017987111","https://openalex.org/W2032005532","https://openalex.org/W2034248602","https://openalex.org/W2039130732","https://openalex.org/W2043936496","https://openalex.org/W2057197276","https://openalex.org/W2066459155","https://openalex.org/W2070783909","https://openalex.org/W2076327797","https://openalex.org/W2088169690","https://openalex.org/W2096217494","https://openalex.org/W2096710051","https://openalex.org/W2103437658","https://openalex.org/W2106084579","https://openalex.org/W2108169091","https://openalex.org/W2115224625","https://openalex.org/W2128657381","https://openalex.org/W2141860564","https://openalex.org/W2149283764","https://openalex.org/W2152687999","https://openalex.org/W2154791587","https://openalex.org/W2155421090","https://openalex.org/W2167213787","https://openalex.org/W2317938141","https://openalex.org/W3022776974","https://openalex.org/W3100333039","https://openalex.org/W3105364218","https://openalex.org/W4243998378","https://openalex.org/W4301388242","https://openalex.org/W4301425558"],"related_works":["https://openalex.org/W2121302585","https://openalex.org/W4367054330","https://openalex.org/W2041440059","https://openalex.org/W4233225079","https://openalex.org/W2141576921","https://openalex.org/W174833456","https://openalex.org/W2168982440","https://openalex.org/W51447970","https://openalex.org/W659271869","https://openalex.org/W2123226256"],"abstract_inverted_index":{"Detection":[0],"of":[1,4,28,41,47,60,91,94,99,110,128],"the":[2,22,29,48,58,61,92,105,111,119],"number":[3,93],"signals":[5],"embedded":[6],"in":[7,13],"noise":[8],"is":[9,32],"a":[10,37,70,86,97],"fundamental":[11],"problem":[12],"signal":[14,49],"and":[15,57,107],"array":[16,30],"processing.":[17],"This":[18],"paper":[19],"focuses":[20],"on":[21],"non-parametric":[23],"setting":[24],"where":[25,68],"no":[26],"knowledge":[27],"manifold":[31],"assumed.":[33],"First,":[34],"we":[35,84],"present":[36,85],"detailed":[38],"statistical":[39],"analysis":[40,46,76],"this":[42,75],"problem,":[43],"including":[44],"an":[45],"strength":[50],"required":[51],"for":[52,89],"detection":[53,63,90,108],"with":[54,77],"high":[55],"probability,":[56],"form":[59],"optimal":[62],"test":[64,71],"under":[65],"certain":[66],"conditions":[67],"such":[69],"exists.":[72],"Second,":[73],"combining":[74],"recent":[78],"results":[79],"from":[80],"random":[81],"matrix":[82],"theory,":[83],"new":[87],"algorithm":[88],"sources":[95],"via":[96],"sequence":[98],"hypothesis":[100],"tests.":[101],"We":[102],"theoretically":[103],"analyze":[104],"consistency":[106],"performance":[109],"proposed":[112],"algorithm,":[113],"showing":[114],"its":[115],"superiority":[116],"compared":[117],"to":[118],"standard":[120],"minimum":[121],"description":[122],"length":[123],"(MDL)-based":[124],"estimator.":[125],"A":[126],"series":[127],"simulations":[129],"confirm":[130],"our":[131],"theoretical":[132],"analysis.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":24},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":26},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":24},{"year":2012,"cited_by_count":19}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}