Some statistical applications of Faa di Bruno
The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503–520]. We next derive some u...
Gespeichert in:
| Veröffentlicht in: | Journal of multivariate analysis 2006-11, Vol.97 (10), p.2131-2140 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2140 |
|---|---|
| container_issue | 10 |
| container_start_page | 2131 |
| container_title | Journal of multivariate analysis |
| container_volume | 97 |
| creator | Savits, Thomas H. |
| description | The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503–520]. We next derive some useful recursion formulas. These results are then applied to obtain both explicit expressions and recursive formulas for the multivariate Hermite polynomials and moments associated with a multivariate normal distribution. Finally, an explicit expression is derived for the formal Edgeworth series expansion of the distribution of a normalized sum of iid random variables. |
| doi_str_mv | 10.1016/j.jmva.2006.03.001 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_218693023</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0047259X06000340</els_id><sourcerecordid>1166714011</sourcerecordid><originalsourceid>FETCH-LOGICAL-c471t-9dc3cb8bca2470717f0a01eed1a107e4913637d541b007b31eedb208923fa5863</originalsourceid><addsrcrecordid>eNp9UMFq3DAQFSWFbtL-QE8mkKPdGcm2bMilXbJpICGHpNCbGMtjKrNru5J3Yf8-cjektxxmJEbvPb15QnxFyBCw_NZn_e5AmQQoM1AZAH4QK4S6SLXM1ZlYAeQ6lUX9-5M4D6GPACx0vhLp07jjJMw0uzA7S9uEpmkbL7Mbh5CMXbIhSlqX_PD7YfwsPna0Dfzl9bwQvzY3z-uf6f3j7d36-31qc41zWrdW2aZqLMlcg0bdAQEyt0gImvMaVal0W-TYAOhGLU-NhKqWqqOiKtWFuDzpTn78u-cwm37c-yF-aSRWZa1AqgiSJ5D1YwieOzN5tyN_NAhmScX0ZknFLKkYUCYuHUkPJ5Lnie0bg5kX6EDmYBTVOrZjrH9MRS5W1FQ0LTNUGF3kYP7Mu6h39eqUQkyv8zRYF_47qWQRDS8bXZ9wHGM7OPYmWMeD5dZ5trNpR_ee7RdLi4-V</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>218693023</pqid></control><display><type>article</type><title>Some statistical applications of Faa di Bruno</title><source>RePEc</source><source>Elsevier ScienceDirect Journals Complete</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Savits, Thomas H.</creator><creatorcontrib>Savits, Thomas H.</creatorcontrib><description>The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503–520]. We next derive some useful recursion formulas. These results are then applied to obtain both explicit expressions and recursive formulas for the multivariate Hermite polynomials and moments associated with a multivariate normal distribution. Finally, an explicit expression is derived for the formal Edgeworth series expansion of the distribution of a normalized sum of iid random variables.</description><identifier>ISSN: 0047-259X</identifier><identifier>EISSN: 1095-7243</identifier><identifier>DOI: 10.1016/j.jmva.2006.03.001</identifier><identifier>CODEN: JMVAAI</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>Edgeworth expansions ; Exact sciences and technology ; Faa di Bruno ; Faa di Bruno Hermite polynomials Edgeworth expansions ; Hermite polynomials ; Mathematics ; Multivariate analysis ; Polynomials ; Probability and statistics ; Random variables ; Recursive algorithms ; Sciences and techniques of general use ; Statistics ; Studies</subject><ispartof>Journal of multivariate analysis, 2006-11, Vol.97 (10), p.2131-2140</ispartof><rights>2006 Elsevier Inc.</rights><rights>2006 INIST-CNRS</rights><rights>Copyright Taylor & Francis Group Nov 2006</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c471t-9dc3cb8bca2470717f0a01eed1a107e4913637d541b007b31eedb208923fa5863</citedby><cites>FETCH-LOGICAL-c471t-9dc3cb8bca2470717f0a01eed1a107e4913637d541b007b31eedb208923fa5863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0047259X06000340$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,3994,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18251866$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeejmvana/v_3a97_3ay_3a2006_3ai_3a10_3ap_3a2131-2140.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Savits, Thomas H.</creatorcontrib><title>Some statistical applications of Faa di Bruno</title><title>Journal of multivariate analysis</title><description>The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503–520]. We next derive some useful recursion formulas. These results are then applied to obtain both explicit expressions and recursive formulas for the multivariate Hermite polynomials and moments associated with a multivariate normal distribution. Finally, an explicit expression is derived for the formal Edgeworth series expansion of the distribution of a normalized sum of iid random variables.</description><subject>Edgeworth expansions</subject><subject>Exact sciences and technology</subject><subject>Faa di Bruno</subject><subject>Faa di Bruno Hermite polynomials Edgeworth expansions</subject><subject>Hermite polynomials</subject><subject>Mathematics</subject><subject>Multivariate analysis</subject><subject>Polynomials</subject><subject>Probability and statistics</subject><subject>Random variables</subject><subject>Recursive algorithms</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><subject>Studies</subject><issn>0047-259X</issn><issn>1095-7243</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNp9UMFq3DAQFSWFbtL-QE8mkKPdGcm2bMilXbJpICGHpNCbGMtjKrNru5J3Yf8-cjektxxmJEbvPb15QnxFyBCw_NZn_e5AmQQoM1AZAH4QK4S6SLXM1ZlYAeQ6lUX9-5M4D6GPACx0vhLp07jjJMw0uzA7S9uEpmkbL7Mbh5CMXbIhSlqX_PD7YfwsPna0Dfzl9bwQvzY3z-uf6f3j7d36-31qc41zWrdW2aZqLMlcg0bdAQEyt0gImvMaVal0W-TYAOhGLU-NhKqWqqOiKtWFuDzpTn78u-cwm37c-yF-aSRWZa1AqgiSJ5D1YwieOzN5tyN_NAhmScX0ZknFLKkYUCYuHUkPJ5Lnie0bg5kX6EDmYBTVOrZjrH9MRS5W1FQ0LTNUGF3kYP7Mu6h39eqUQkyv8zRYF_47qWQRDS8bXZ9wHGM7OPYmWMeD5dZ5trNpR_ee7RdLi4-V</recordid><startdate>20061101</startdate><enddate>20061101</enddate><creator>Savits, Thomas H.</creator><general>Elsevier Inc</general><general>Elsevier</general><general>Taylor & Francis LLC</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20061101</creationdate><title>Some statistical applications of Faa di Bruno</title><author>Savits, Thomas H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c471t-9dc3cb8bca2470717f0a01eed1a107e4913637d541b007b31eedb208923fa5863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Edgeworth expansions</topic><topic>Exact sciences and technology</topic><topic>Faa di Bruno</topic><topic>Faa di Bruno Hermite polynomials Edgeworth expansions</topic><topic>Hermite polynomials</topic><topic>Mathematics</topic><topic>Multivariate analysis</topic><topic>Polynomials</topic><topic>Probability and statistics</topic><topic>Random variables</topic><topic>Recursive algorithms</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Savits, Thomas H.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Journal of multivariate analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Savits, Thomas H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some statistical applications of Faa di Bruno</atitle><jtitle>Journal of multivariate analysis</jtitle><date>2006-11-01</date><risdate>2006</risdate><volume>97</volume><issue>10</issue><spage>2131</spage><epage>2140</epage><pages>2131-2140</pages><issn>0047-259X</issn><eissn>1095-7243</eissn><coden>JMVAAI</coden><abstract>The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503–520]. We next derive some useful recursion formulas. These results are then applied to obtain both explicit expressions and recursive formulas for the multivariate Hermite polynomials and moments associated with a multivariate normal distribution. Finally, an explicit expression is derived for the formal Edgeworth series expansion of the distribution of a normalized sum of iid random variables.</abstract><cop>San Diego, CA</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jmva.2006.03.001</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0047-259X |
| ispartof | Journal of multivariate analysis, 2006-11, Vol.97 (10), p.2131-2140 |
| issn | 0047-259X 1095-7243 |
| language | eng |
| recordid | cdi_proquest_journals_218693023 |
| source | RePEc; Elsevier ScienceDirect Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Edgeworth expansions Exact sciences and technology Faa di Bruno Faa di Bruno Hermite polynomials Edgeworth expansions Hermite polynomials Mathematics Multivariate analysis Polynomials Probability and statistics Random variables Recursive algorithms Sciences and techniques of general use Statistics Studies |
| title | Some statistical applications of Faa di Bruno |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-12T16%3A30%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Some%20statistical%20applications%20of%20Faa%20di%20Bruno&rft.jtitle=Journal%20of%20multivariate%20analysis&rft.au=Savits,%20Thomas%20H.&rft.date=2006-11-01&rft.volume=97&rft.issue=10&rft.spage=2131&rft.epage=2140&rft.pages=2131-2140&rft.issn=0047-259X&rft.eissn=1095-7243&rft.coden=JMVAAI&rft_id=info:doi/10.1016/j.jmva.2006.03.001&rft_dat=%3Cproquest_cross%3E1166714011%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=218693023&rft_id=info:pmid/&rft_els_id=S0047259X06000340&rfr_iscdi=true |