{"id":"https://openalex.org/W4415001468","doi":"https://doi.org/10.1007/s11222-025-10744-1","title":"The effective number of parameters in kernel density estimation","display_name":"The effective number of parameters in kernel density estimation","publication_year":2025,"publication_date":"2025-10-09","ids":{"openalex":"https://openalex.org/W4415001468","doi":"https://doi.org/10.1007/s11222-025-10744-1"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-025-10744-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10744-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10744-1.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10744-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5099380852","display_name":"Sofia Guglielmini","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Sofia Guglielmini","raw_affiliation_strings":["Faculty of Economics and Business, KU Leuven, Naamsestraat 69, 3000, Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Faculty of Economics and Business, KU Leuven, Naamsestraat 69, 3000, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104478235","display_name":"I. Volobouev","orcid":"https://orcid.org/0000-0002-2087-6128"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Igor Volobouev","raw_affiliation_strings":["Department of Department of Physics & Astronomy, Texas Tech University, Lubbock, TX, 79409-1042, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Department of Physics & Astronomy, Texas Tech University, Lubbock, TX, 79409-1042, U.S.A","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005707213","display_name":"A. Alexandre Trindade","orcid":"https://orcid.org/0000-0003-3133-5623"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Alexandre Trindade","raw_affiliation_strings":["Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, 79409-1042, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX, 79409-1042, U.S.A","institution_ids":["https://openalex.org/I12315562"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5099380852"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26076992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9901000261306763,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9901000261306763,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9721999764442444,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9053999781608582,"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/kernel-density-estimation","display_name":"Kernel density estimation","score":0.6241000294685364},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5687000155448914},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.5350000262260437},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.4406999945640564},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.4120999872684479},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.40540000796318054},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.38589999079704285},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.3668999969959259}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7799000144004822},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.6241000294685364},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5687000155448914},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.5350000262260437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4738999903202057},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4406999945640564},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41119998693466187},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.40540000796318054},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.38589999079704285},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.3668999969959259},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3319999873638153},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.2971999943256378},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C21596040","wikidata":"https://www.wikidata.org/wiki/Q2896771","display_name":"Unimodality","level":2,"score":0.2648000121116638}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11222-025-10744-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10744-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10744-1.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11222-025-10744-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10744-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10744-1.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5197874712","display_name":null,"funder_award_id":"DE-SC0015592","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415001468.pdf","grobid_xml":"https://content.openalex.org/works/W4415001468.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1502338185","https://openalex.org/W1593505867","https://openalex.org/W1967969088","https://openalex.org/W1995514448","https://openalex.org/W1996908140","https://openalex.org/W1997927050","https://openalex.org/W1999058847","https://openalex.org/W2118020555","https://openalex.org/W2153464267","https://openalex.org/W2166949820","https://openalex.org/W2293533096","https://openalex.org/W2978542011","https://openalex.org/W3104298728","https://openalex.org/W4229938797","https://openalex.org/W4238717354","https://openalex.org/W4243863038","https://openalex.org/W4248721357","https://openalex.org/W4254769327"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1],"devise":[2],"a":[3,46,72,79,128,138,153],"new":[4,47,129,154],"formula":[5],"for":[6,27],"measuring":[7],"the":[8,21,28,31,34,42,56,63,86,92,150],"effective":[9],"degrees":[10],"of":[11,30,62,83,91,111,152],"freedom":[12],"(EDoF)":[13],"in":[14],"kernel":[15,43,73],"density":[16],"estimation":[17],"(KDE).":[18],"Starting":[19],"from":[20,137],"orthogonal":[22],"polynomial":[23],"sequence":[24],"(OPS)":[25],"expansion":[26,60],"ratio":[29],"empirical":[32,106],"to":[33,45,51,78,119,146],"oracle":[35,81,140],"density,":[36],"we":[37],"show":[38],"how":[39],"convolution":[40,147],"with":[41,49,104],"leads":[44,77],"OPS":[48,65],"respect":[50],"which":[52,76,135],"one":[53],"may":[54],"express":[55],"resulting":[57],"KDE.":[58],"The":[59,133],"coefficients":[61],"two":[64],"systems":[66],"can":[67],"then":[68],"be":[69],"related":[70],"via":[71],"sensitivity":[74],"matrix,":[75],"natural":[80],"definition":[82],"EDoF":[84,95],"through":[85,99],"trace":[87],"operator.":[88],"Asymptotic":[89],"properties":[90],"(empirical)":[93],"plug-in":[94],"are":[96,108],"worked":[97],"out":[98],"influence":[100],"functions,":[101],"and":[102,142],"connections":[103],"other":[105],"EDoFs":[107],"established.":[109],"Minimization":[110],"Kullback-Leibler":[112],"divergence":[113],"is":[114,143],"investigated":[115],"as":[116,164],"an":[117,160],"alternative":[118],"integrated":[120],"squared":[121],"error":[122],"based":[123,158],"bandwidth":[124,155],"selection":[125,156],"rules,":[126],"yielding":[127],"normal":[130],"scale":[131],"rule.":[132],"methodology,":[134],"arises":[136],"proper":[139],"formulation":[141],"not":[144],"restricted":[145],"kernels,":[148],"suggests":[149],"possibility":[151],"rule":[157],"on":[159],"information":[161],"criterion":[162],"such":[163],"AIC.":[165]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
