{"id":"https://openalex.org/W61473168","doi":"https://doi.org/10.1214/09-lnms5709","title":"Nonparametric Estimation for L\u00e9vy Models Based on Discrete-Sampling","display_name":"Nonparametric Estimation for L\u00e9vy Models Based on Discrete-Sampling","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W61473168","doi":"https://doi.org/10.1214/09-lnms5709","mag":"61473168"},"language":"en","primary_location":{"id":"doi:10.1214/09-lnms5709","doi":"https://doi.org/10.1214/09-lnms5709","is_oa":true,"landing_page_url":"https://doi.org/10.1214/09-lnms5709","pdf_url":"https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/Optimality/chapter/Nonparametric-Estimation-for-L%c3%a9vy-Models-Based-on-Discrete-Sampling/10.1214/09-LNMS5709.pdf","source":{"id":"https://openalex.org/S4210235996","display_name":"Lecture notes-monograph series","issn_l":"0749-2170","issn":["0749-2170","2328-3874"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Institute of Mathematical Statistics Lecture Notes - Monograph Series","raw_type":"book-chapter"},"volume":null,"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/Optimality/chapter/Nonparametric-Estimation-for-L%c3%a9vy-Models-Based-on-Discrete-Sampling/10.1214/09-LNMS5709.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050581969","display_name":"Jos\u00e9 Enrique Figueroa-l\u00f3pez","orcid":"https://orcid.org/0000-0002-7357-0341","observed_orcids":["https://orcid.org/0000-0002-7357-0341"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 E. Figueroa-L\u00f3pez","raw_affiliation_strings":["Department of Statistics, Purdue University, West Lafayette, IN 47906,","Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Purdue University, West Lafayette, IN 47906,","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050581969"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":20.2548,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.99147243,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"117","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.0012000000569969416,"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/T13500","display_name":"Probability and Statistical Research","score":0.0010999999940395355,"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/levy-models","display_name":"L\u00e9vy models","score":0.8050000071525574},{"id":"https://openalex.org/keywords/nonparametric-estimation","display_name":"nonparametric estimation","score":0.890999972820282},{"id":"https://openalex.org/keywords/discrete-sampling","display_name":"discrete sampling","score":0.8370000123977661},{"id":"https://openalex.org/keywords/sieve-estimation","display_name":"sieve estimation","score":0.6060000061988831},{"id":"https://openalex.org/keywords/minimax-rates-of-convergence","display_name":"minimax rates of convergence","score":0.7950000166893005},{"id":"https://openalex.org/keywords/sampling-rate","display_name":"sampling frequency","score":0.7620000243186951},{"id":"https://openalex.org/keywords/compound-poisson-process","display_name":"compound Poisson process","score":0.7710000276565552},{"id":"https://openalex.org/keywords/variance-gamma-process","display_name":"variance gamma process","score":0.8889999985694885},{"id":"https://openalex.org/keywords/jump-processes","display_name":"jump processes","score":0.5090000033378601},{"id":"https://openalex.org/keywords/brownian-motion-with-drift","display_name":"Brownian motion with drift","score":0.949999988079071}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7434231042861938},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6432763338088989},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6131489872932434},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.6107217073440552},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5449756979942322},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5234800577163696},{"id":"https://openalex.org/C17732976","wikidata":"https://www.wikidata.org/wiki/Q7511782","display_name":"Sieve (category theory)","level":2,"score":0.498767614364624},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4914301633834839},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.4607774615287781},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.440371036529541},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.4389500617980957},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.42483651638031006},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3827185034751892},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27017927169799805},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2636988162994385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14059856534004211},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1378692388534546},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1214/09-lnms5709","doi":"https://doi.org/10.1214/09-lnms5709","is_oa":true,"landing_page_url":"https://doi.org/10.1214/09-lnms5709","pdf_url":"https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/Optimality/chapter/Nonparametric-Estimation-for-L%c3%a9vy-Models-Based-on-Discrete-Sampling/10.1214/09-LNMS5709.pdf","source":{"id":"https://openalex.org/S4210235996","display_name":"Lecture notes-monograph series","issn_l":"0749-2170","issn":["0749-2170","2328-3874"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Institute of Mathematical Statistics Lecture Notes - Monograph Series","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.369.6706","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.6706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.purdue.edu/~figueroa/Papers/MdlSlctn.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1214/09-lnms5709","doi":"https://doi.org/10.1214/09-lnms5709","is_oa":true,"landing_page_url":"https://doi.org/10.1214/09-lnms5709","pdf_url":"https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/Optimality/chapter/Nonparametric-Estimation-for-L%c3%a9vy-Models-Based-on-Discrete-Sampling/10.1214/09-LNMS5709.pdf","source":{"id":"https://openalex.org/S4210235996","display_name":"Lecture notes-monograph series","issn_l":"0749-2170","issn":["0749-2170","2328-3874"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Institute of Mathematical Statistics Lecture Notes - Monograph Series","raw_type":"book-chapter"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W61473168.pdf","grobid_xml":"https://content.openalex.org/works/W61473168.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W16827625","https://openalex.org/W568726942","https://openalex.org/W1495578089","https://openalex.org/W1499969990","https://openalex.org/W1521617046","https://openalex.org/W1555033159","https://openalex.org/W1562951830","https://openalex.org/W1580334350","https://openalex.org/W1757984443","https://openalex.org/W1965967625","https://openalex.org/W1980519218","https://openalex.org/W1983135873","https://openalex.org/W1996268356","https://openalex.org/W1997989248","https://openalex.org/W1998292733","https://openalex.org/W2009431235","https://openalex.org/W2013286469","https://openalex.org/W2052066969","https://openalex.org/W2068365256","https://openalex.org/W2084029876","https://openalex.org/W2100190417","https://openalex.org/W2101157574","https://openalex.org/W2125862561","https://openalex.org/W2138540172","https://openalex.org/W2168891962","https://openalex.org/W2797641211","https://openalex.org/W3121574170","https://openalex.org/W4205354563","https://openalex.org/W4293859755"],"related_works":["https://openalex.org/W3098468091","https://openalex.org/W7098493070","https://openalex.org/W7095231461","https://openalex.org/W7100116336","https://openalex.org/W2067801276","https://openalex.org/W7098457611","https://openalex.org/W1538089293","https://openalex.org/W4390852222","https://openalex.org/W4404344799","https://openalex.org/W2268751576"],"abstract_inverted_index":{"<!--":[0],"***":[1,4],"Custom":[2],"HTML":[3],"-->":[5],"A":[6],"L\u00e9vy":[7,30,78,110],"model":[8],"combines":[9],"a":[10,16,22,45,90,117,159],"Brownian":[11],"motion":[12],"with":[13],"drift":[14],"and":[15,103,164],"pure-jump":[17],"homogeneous":[18],"process":[19,115],"such":[20],"as":[21,101],"compound":[23],"Poisson":[24],"process.":[25,178],"The":[26,85,179,192],"estimation":[27,150,168],"of":[28,39,67,83,88,137,144,146,149,162,176,203],"the":[29,32,36,40,51,65,77,109,114,123,135,138,142,147,152,155,167,172,177,185,201],"density,":[31],"infinite-dimensional":[33],"parameter":[34],"controlling":[35],"jump":[37],"dynamics":[38],"process,":[41],"is":[42,94,131,154,189,195],"studied":[43],"under":[44],"discrete-sampling":[46],"scheme.":[47],"In":[48],"that":[49,129,141],"case,":[50],"jumps":[52],"are":[53],"latent":[54],"variables":[55],"whose":[56],"statistical":[57],"properties":[58],"can":[59],"in":[60,200],"principle":[61],"be":[62],"assessed":[63],"when":[64],"frequency":[66,120,181],"observations":[68],"increase":[69],"to":[70,122,133,183],"infinity.":[71],"We":[72],"propose":[73],"nonparametric":[74],"estimators":[75],"for":[76],"density":[79],"following":[80],"Grenander\u2019s":[81],"method":[82,194],"sieves.":[84],"associated":[86],"problem":[87],"selecting":[89],"suitable":[91],"approximating":[92],"sieve":[93,139],"subsequently":[95],"investigated":[96],"using":[97],"regular":[98],"piece-wise":[99],"polynomials":[100],"sieves":[102],"assuming":[104],"standard":[105],"smoothness":[106],"conditions":[107],"on":[108,171],"density.":[111],"By":[112],"sampling":[113,180],"at":[116],"high":[118],"enough":[119],"relative":[121],"time":[124],"horizon":[125],"T,":[126],"we":[127],"show":[128],"it":[130],"feasible":[132],"choose":[134],"dimension":[136],"so":[140],"rate":[143,188],"convergence":[145],"risk":[148],"off":[151],"origin":[153],"best":[156],"possible":[157],"from":[158],"minimax":[160,187],"point":[161],"view,":[163],"even":[165],"if":[166],"were":[169],"based":[170],"whole":[173],"sample":[174],"path":[175],"necessary":[182],"attain":[184],"optimal":[186],"explicitly":[190],"identified.":[191],"proposed":[193],"illustrated":[196],"by":[197],"simulation":[198],"experiments":[199],"case":[202],"variance":[204],"Gamma":[205],"processes.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}