Edgeworth expansions for triangular arrays
The Edgeworth expansion techniques are used to develop asymptotic expansions that approximate the distribution function for a general class of statistics, appearing as sums or appropriately smooth functions of sums of i.i.d. and non-lattice random vectors, under Cramér's condition and the exist...
Gespeichert in:
| Veröffentlicht in: | Communications in statistics. Theory and methods 1998-01, Vol.27 (3), p.705-722 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 722 |
|---|---|
| container_issue | 3 |
| container_start_page | 705 |
| container_title | Communications in statistics. Theory and methods |
| container_volume | 27 |
| creator | García-Soidán, Pilar H |
| description | The Edgeworth expansion techniques are used to develop asymptotic expansions that approximate the distribution function for a general class of statistics, appearing as sums or appropriately smooth functions of sums of i.i.d. and non-lattice random vectors, under Cramér's condition and the existence of moments up to a certain order. To mimic this technique in the context of triangular arrays, the requirements to guarantee the existence of asymptotic expansions shall take into account the dependence on the sample size n of the distribution function of the random vectors in this context; in particular, the traditional Cramir's condition will be replaced by a modified version, in terms of n, as suggested in Hall (1991) for kernel-type density estimation. Formal expansions will be derived if enough order moments are bounded, paying particular attention to the second order moments. |
| doi_str_mv | 10.1080/03610929808832122 |
| format | Article |
| fullrecord | <record><control><sourceid>pascalfrancis_cross</sourceid><recordid>TN_cdi_pascalfrancis_primary_2205282</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2205282</sourcerecordid><originalsourceid>FETCH-LOGICAL-c325t-e2172537565ba16855a619eea1cdd67476df37897c17564a92dc978857b60133</originalsourceid><addsrcrecordid>eNqFj01Lw0AQQBdRMFZ_gLccPAnRnd3sF3iRUj-g4KUHb2G62dRImpTdiM2_d0PUSxFPc5j3hnmEXAK9AarpLeUSqGFGU605A8aOSAKCsywH8XpMknGfRUCekrMQ3ikFoTRPyPWi3LjPzvdvqdvvsA1114a06nza-xrbzUeDPkXvcQjn5KTCJriL7zkjq4fFav6ULV8en-f3y8xyJvrMMVBMcCWkWCNILQRKMM4h2LKUKleyrLjSRlmITI6GldYorYVaSwqczwhMZ63vQvCuKna-3qIfCqDF2FoctEbnanJ2GCw2lcfW1uFXZIwKpkdMTVjdxsItxu6mLHocms7_OAfHi37fR_PuX5P__d8XxDJ3JA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Edgeworth expansions for triangular arrays</title><source>Taylor & Francis Journals Complete</source><creator>García-Soidán, Pilar H</creator><creatorcontrib>García-Soidán, Pilar H</creatorcontrib><description>The Edgeworth expansion techniques are used to develop asymptotic expansions that approximate the distribution function for a general class of statistics, appearing as sums or appropriately smooth functions of sums of i.i.d. and non-lattice random vectors, under Cramér's condition and the existence of moments up to a certain order. To mimic this technique in the context of triangular arrays, the requirements to guarantee the existence of asymptotic expansions shall take into account the dependence on the sample size n of the distribution function of the random vectors in this context; in particular, the traditional Cramir's condition will be replaced by a modified version, in terms of n, as suggested in Hall (1991) for kernel-type density estimation. Formal expansions will be derived if enough order moments are bounded, paying particular attention to the second order moments.</description><identifier>ISSN: 0361-0926</identifier><identifier>EISSN: 1532-415X</identifier><identifier>DOI: 10.1080/03610929808832122</identifier><identifier>CODEN: CSTMDC</identifier><language>eng</language><publisher>Philadelphia, PA: Marcel Dekker, Inc</publisher><subject>Cramér' condition: non lattice random vector ; Distribution theory ; Exact sciences and technology ; Mathematics ; Nonparametric inference ; Probability and statistics ; Sciences and techniques of general use ; Statistics</subject><ispartof>Communications in statistics. Theory and methods, 1998-01, Vol.27 (3), p.705-722</ispartof><rights>Copyright Taylor & Francis Group, LLC 1998</rights><rights>1998 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c325t-e2172537565ba16855a619eea1cdd67476df37897c17564a92dc978857b60133</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/03610929808832122$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/03610929808832122$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,780,784,4024,27923,27924,27925,59647,60436</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2205282$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>García-Soidán, Pilar H</creatorcontrib><title>Edgeworth expansions for triangular arrays</title><title>Communications in statistics. Theory and methods</title><description>The Edgeworth expansion techniques are used to develop asymptotic expansions that approximate the distribution function for a general class of statistics, appearing as sums or appropriately smooth functions of sums of i.i.d. and non-lattice random vectors, under Cramér's condition and the existence of moments up to a certain order. To mimic this technique in the context of triangular arrays, the requirements to guarantee the existence of asymptotic expansions shall take into account the dependence on the sample size n of the distribution function of the random vectors in this context; in particular, the traditional Cramir's condition will be replaced by a modified version, in terms of n, as suggested in Hall (1991) for kernel-type density estimation. Formal expansions will be derived if enough order moments are bounded, paying particular attention to the second order moments.</description><subject>Cramér' condition: non lattice random vector</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>Mathematics</subject><subject>Nonparametric inference</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><issn>0361-0926</issn><issn>1532-415X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><recordid>eNqFj01Lw0AQQBdRMFZ_gLccPAnRnd3sF3iRUj-g4KUHb2G62dRImpTdiM2_d0PUSxFPc5j3hnmEXAK9AarpLeUSqGFGU605A8aOSAKCsywH8XpMknGfRUCekrMQ3ikFoTRPyPWi3LjPzvdvqdvvsA1114a06nza-xrbzUeDPkXvcQjn5KTCJriL7zkjq4fFav6ULV8en-f3y8xyJvrMMVBMcCWkWCNILQRKMM4h2LKUKleyrLjSRlmITI6GldYorYVaSwqczwhMZ63vQvCuKna-3qIfCqDF2FoctEbnanJ2GCw2lcfW1uFXZIwKpkdMTVjdxsItxu6mLHocms7_OAfHi37fR_PuX5P__d8XxDJ3JA</recordid><startdate>19980101</startdate><enddate>19980101</enddate><creator>García-Soidán, Pilar H</creator><general>Marcel Dekker, Inc</general><general>Taylor & Francis</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19980101</creationdate><title>Edgeworth expansions for triangular arrays</title><author>García-Soidán, Pilar H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-e2172537565ba16855a619eea1cdd67476df37897c17564a92dc978857b60133</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Cramér' condition: non lattice random vector</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>Mathematics</topic><topic>Nonparametric inference</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>García-Soidán, Pilar H</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Communications in statistics. Theory and methods</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>García-Soidán, Pilar H</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Edgeworth expansions for triangular arrays</atitle><jtitle>Communications in statistics. Theory and methods</jtitle><date>1998-01-01</date><risdate>1998</risdate><volume>27</volume><issue>3</issue><spage>705</spage><epage>722</epage><pages>705-722</pages><issn>0361-0926</issn><eissn>1532-415X</eissn><coden>CSTMDC</coden><abstract>The Edgeworth expansion techniques are used to develop asymptotic expansions that approximate the distribution function for a general class of statistics, appearing as sums or appropriately smooth functions of sums of i.i.d. and non-lattice random vectors, under Cramér's condition and the existence of moments up to a certain order. To mimic this technique in the context of triangular arrays, the requirements to guarantee the existence of asymptotic expansions shall take into account the dependence on the sample size n of the distribution function of the random vectors in this context; in particular, the traditional Cramir's condition will be replaced by a modified version, in terms of n, as suggested in Hall (1991) for kernel-type density estimation. Formal expansions will be derived if enough order moments are bounded, paying particular attention to the second order moments.</abstract><cop>Philadelphia, PA</cop><pub>Marcel Dekker, Inc</pub><doi>10.1080/03610929808832122</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0361-0926 |
| ispartof | Communications in statistics. Theory and methods, 1998-01, Vol.27 (3), p.705-722 |
| issn | 0361-0926 1532-415X |
| language | eng |
| recordid | cdi_pascalfrancis_primary_2205282 |
| source | Taylor & Francis Journals Complete |
| subjects | Cramér' condition: non lattice random vector Distribution theory Exact sciences and technology Mathematics Nonparametric inference Probability and statistics Sciences and techniques of general use Statistics |
| title | Edgeworth expansions for triangular arrays |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T15%3A46%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-pascalfrancis_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Edgeworth%20expansions%20for%20triangular%20arrays&rft.jtitle=Communications%20in%20statistics.%20Theory%20and%20methods&rft.au=Garc%C3%ADa-Soid%C3%A1n,%20Pilar%20H&rft.date=1998-01-01&rft.volume=27&rft.issue=3&rft.spage=705&rft.epage=722&rft.pages=705-722&rft.issn=0361-0926&rft.eissn=1532-415X&rft.coden=CSTMDC&rft_id=info:doi/10.1080/03610929808832122&rft_dat=%3Cpascalfrancis_cross%3E2205282%3C/pascalfrancis_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |