{"id":"https://openalex.org/W2000493427","doi":"https://doi.org/10.1080/00031305.1999.10474463","title":"Explaining the Saddlepoint Approximation","display_name":"Explaining the Saddlepoint Approximation","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W2000493427","doi":"https://doi.org/10.1080/00031305.1999.10474463","mag":"2000493427"},"language":"en","primary_location":{"id":"doi:10.1080/00031305.1999.10474463","doi":"https://doi.org/10.1080/00031305.1999.10474463","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00031305.1999.10474463","pdf_url":null,"source":{"id":"https://openalex.org/S4179095","display_name":"The American Statistician","issn_l":"0003-1305","issn":["0003-1305","1537-2731"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Statistician","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10016/10734","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Constantino Goutis","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Constantino Goutis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080225575","display_name":"George Casella","orcid":"https://orcid.org/0000-0001-8154-8278","observed_orcids":["https://orcid.org/0000-0001-8154-8278"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Casella","raw_affiliation_strings":["Department of Biometrics, Cornell University, 434 Warren Hall, Ithaca, NY, 14853, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biometrics, Cornell University, 434 Warren Hall, Ithaca, NY, 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.6128,"has_fulltext":false,"cited_by_count":168,"citation_normalized_percentile":{"value":0.95397434,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":92,"max":99},"biblio":{"volume":"53","issue":"3","first_page":"216","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9146000146865845,"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/T13500","display_name":"Probability and Statistical Research","score":0.9146000146865845,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.06700000166893005,"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/T13141","display_name":"Statistical Methods and Applications","score":0.0032999999821186066,"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/saddlepoint-approximation","display_name":"saddlepoint approximation","score":1.0},{"id":"https://openalex.org/keywords/laplace-approximation","display_name":"Laplace approximation","score":0.7509999871253967},{"id":"https://openalex.org/keywords/taylor-expansion","display_name":"Taylor series expansion","score":0.7440000176429749},{"id":"https://openalex.org/keywords/fourier-inversion-formula","display_name":"Fourier inversion","score":0.8389999866485596},{"id":"https://openalex.org/keywords/edgeworth-expansion","display_name":"Edgeworth expansion","score":0.9679999947547913},{"id":"https://openalex.org/keywords/density-estimation","display_name":"density estimation","score":0.7450000047683716},{"id":"https://openalex.org/keywords/maximum-likelihood-estimator","display_name":"maximum likelihood estimator","score":0.9350000023841858},{"id":"https://openalex.org/keywords/exponential-family","display_name":"exponential family","score":0.9769999980926514}],"concepts":[{"id":"https://openalex.org/C160817175","wikidata":"https://www.wikidata.org/wiki/Q5337942","display_name":"Edgeworth series","level":2,"score":0.8337713479995728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7776806354522705},{"id":"https://openalex.org/C22243797","wikidata":"https://www.wikidata.org/wiki/Q2058297","display_name":"Laplace's method","level":3,"score":0.6879473924636841},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6788105964660645},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5677276253700256},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5355225801467896},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5111096501350403},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4978597164154053},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.48144906759262085},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.47321027517318726},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.43434765934944153},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4252530038356781},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.356533944606781},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22356536984443665},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00031305.1999.10474463","doi":"https://doi.org/10.1080/00031305.1999.10474463","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00031305.1999.10474463","pdf_url":null,"source":{"id":"https://openalex.org/S4179095","display_name":"The American Statistician","issn_l":"0003-1305","issn":["0003-1305","1537-2731"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Statistician","raw_type":"journal-article"},{"id":"doi:10.2307/2686100","doi":"https://doi.org/10.2307/2686100","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2686100","pdf_url":null,"source":{"id":"https://openalex.org/S4179095","display_name":"The American Statistician","issn_l":"0003-1305","issn":["0003-1305","1537-2731"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Statistician","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:cte:wsrepe:10734","doi":null,"is_oa":false,"landing_page_url":"https://e-archivo.uc3m.es/rest/api/core/bitstreams/f459ec02-5844-42f5-88dc-b13955a09ff0/content","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"preprint"},{"id":"pmh:oai:e-archivo.uc3m.es:10016/10734","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/10734","pdf_url":null,"source":{"id":"https://openalex.org/S4306400817","display_name":"e-Archivo (Carlos III University of Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I50357001","host_organization_name":"Universidad Carlos III de Madrid","host_organization_lineage":["https://openalex.org/I50357001"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/workingPaper"}],"best_oa_location":{"id":"pmh:oai:e-archivo.uc3m.es:10016/10734","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/10734","pdf_url":null,"source":{"id":"https://openalex.org/S4306400817","display_name":"e-Archivo (Carlos III University of Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I50357001","host_organization_name":"Universidad Carlos III de Madrid","host_organization_lineage":["https://openalex.org/I50357001"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/workingPaper"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2850412646","display_name":"Mathematical Sciences:  Assessing Robustness of Inference","funder_award_id":"9305547","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1959492","https://openalex.org/W12964321","https://openalex.org/W1550833282","https://openalex.org/W1964404845","https://openalex.org/W1975956590","https://openalex.org/W1982547531","https://openalex.org/W1985093013","https://openalex.org/W1986827948","https://openalex.org/W1991503662","https://openalex.org/W1995963238","https://openalex.org/W2000951514","https://openalex.org/W2001144080","https://openalex.org/W2005125330","https://openalex.org/W2006477848","https://openalex.org/W2010437600","https://openalex.org/W2010954392","https://openalex.org/W2014952666","https://openalex.org/W2018261390","https://openalex.org/W2022261649","https://openalex.org/W2043017611","https://openalex.org/W2049361783","https://openalex.org/W2056099894","https://openalex.org/W2064662885","https://openalex.org/W2068172802","https://openalex.org/W2069057356","https://openalex.org/W2072375233","https://openalex.org/W2082357819","https://openalex.org/W2092072918","https://openalex.org/W2097147975","https://openalex.org/W2161339375","https://openalex.org/W2161364915","https://openalex.org/W2314297038","https://openalex.org/W2316985810","https://openalex.org/W2331747324","https://openalex.org/W2462667841","https://openalex.org/W2470896286","https://openalex.org/W2471103507","https://openalex.org/W2512619801","https://openalex.org/W2751862591","https://openalex.org/W2790825170","https://openalex.org/W4210300788","https://openalex.org/W4230173782","https://openalex.org/W4232127862","https://openalex.org/W4238306122","https://openalex.org/W4242782598","https://openalex.org/W4248622249","https://openalex.org/W4253934678","https://openalex.org/W4292403327","https://openalex.org/W4293508155","https://openalex.org/W4298443330","https://openalex.org/W4299432846"],"related_works":["https://openalex.org/W7095310668","https://openalex.org/W2010175708","https://openalex.org/W2177707911","https://openalex.org/W2231528777","https://openalex.org/W2049361783","https://openalex.org/W2099853252","https://openalex.org/W2008667625","https://openalex.org/W4388254874","https://openalex.org/W4234719789","https://openalex.org/W4238346371"],"abstract_inverted_index":{"Saddlepoint":[0],"approximations":[1,38],"are":[2,39],"powerful":[3],"tools":[4],"for":[5,9,97],"obtaining":[6],"accurate":[7],"expressions":[8],"densities":[10],"and":[11,19,29,63,92],"distribution":[12],"functions.":[13],"We":[14,49,79],"give":[15],"an":[16],"elementary":[17],"motivation":[18],"explanation":[20],"of":[21,35,43,46,74,84,88,101],"approximation":[22,34,55,70],"techniques,":[23],"starting":[24],"with":[25,41],"Taylor":[26],"series":[27],"expansions":[28],"progressing":[30],"to":[31,52,71],"the":[32,44,53,59,68,72,82,85,95,99],"Laplace":[33],"integrals.":[36],"These":[37],"illustrated":[40],"examples":[42],"convolution":[45],"simple":[47],"densities.":[48],"then":[50],"turn":[51],"saddlepoint":[54,69],"and,":[56],"using":[57],"both":[58],"Fourier":[60],"inversion":[61],"formula":[62],"Edgeworth":[64],"expansions,":[65],"we":[66],"derive":[67],"density":[73,83,100],"a":[75,102],"single":[76],"random":[77,90],"variable.":[78],"next":[80],"approximate":[81],"sample":[86],"mean":[87],"iid":[89],"variables,":[91],"also":[93],"demonstrate":[94],"technique":[96],"approximating":[98],"maximum":[103],"likelihood":[104],"estimator":[105],"in":[106],"exponential":[107],"families.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}