Parameters estimation for asymmetric bifurcating autoregressive processes with missing data
We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process le...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2011-09 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Benoîte de Saporta Gégout-Petit, Anne Marsalle, Laurence |
| description | We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality. |
| doi_str_mv | 10.48550/arxiv.1012.2012 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1012_2012</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2086714660</sourcerecordid><originalsourceid>FETCH-LOGICAL-a510-9032c412bcd1e1bdae0c0290a5a643c6fbb1525c965c99f715b3608f5da2142b3</originalsourceid><addsrcrecordid>eNotUMtOwzAQtJCQqErvnJAlzgnrdewmR1TxqFQJDr1xiNaOU1yRpthJoX-PSznsQzuj1cwwdiMgL0ql4J7Cjz_kAgTmmNoFm6CUIisLxCs2i3ELAKjnqJScsPc3CtS5wYXIXRx8R4Pvd7ztA6d47BISvOXGt2OwCdptOI1DH9wmuBj9wfF96G1aXeTffvjgnU_nxGpooGt22dJndLP_OWXrp8f14iVbvT4vFw-rjJSArAKJthBobCOcMA05sIAVkCJdSKtbY4RCZSudqmrnQhmpoWxVQygKNHLKbs9v_4zX-5BMhGN9CqA-BZAId2dC0vo1Jpf1th_DLklKeKnnotAa5C_UKV-u</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2086714660</pqid></control><display><type>article</type><title>Parameters estimation for asymmetric bifurcating autoregressive processes with missing data</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Benoîte de Saporta ; Gégout-Petit, Anne ; Marsalle, Laurence</creator><creatorcontrib>Benoîte de Saporta ; Gégout-Petit, Anne ; Marsalle, Laurence</creatorcontrib><description>We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1012.2012</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Autoregressive processes ; Bifurcations ; Branching (mathematics) ; Martingales ; Mathematics - Probability ; Mathematics - Statistics Theory ; Missing data ; Normality ; Parameter estimation ; Regression analysis ; Statistics - Theory ; Stochastic processes</subject><ispartof>arXiv.org, 2011-09</ispartof><rights>2011. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27902</link.rule.ids><backlink>$$Uhttps://doi.org/10.1214/11-EJS643$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.1012.2012$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Benoîte de Saporta</creatorcontrib><creatorcontrib>Gégout-Petit, Anne</creatorcontrib><creatorcontrib>Marsalle, Laurence</creatorcontrib><title>Parameters estimation for asymmetric bifurcating autoregressive processes with missing data</title><title>arXiv.org</title><description>We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.</description><subject>Autoregressive processes</subject><subject>Bifurcations</subject><subject>Branching (mathematics)</subject><subject>Martingales</subject><subject>Mathematics - Probability</subject><subject>Mathematics - Statistics Theory</subject><subject>Missing data</subject><subject>Normality</subject><subject>Parameter estimation</subject><subject>Regression analysis</subject><subject>Statistics - Theory</subject><subject>Stochastic processes</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><sourceid>GOX</sourceid><recordid>eNotUMtOwzAQtJCQqErvnJAlzgnrdewmR1TxqFQJDr1xiNaOU1yRpthJoX-PSznsQzuj1cwwdiMgL0ql4J7Cjz_kAgTmmNoFm6CUIisLxCs2i3ELAKjnqJScsPc3CtS5wYXIXRx8R4Pvd7ztA6d47BISvOXGt2OwCdptOI1DH9wmuBj9wfF96G1aXeTffvjgnU_nxGpooGt22dJndLP_OWXrp8f14iVbvT4vFw-rjJSArAKJthBobCOcMA05sIAVkCJdSKtbY4RCZSudqmrnQhmpoWxVQygKNHLKbs9v_4zX-5BMhGN9CqA-BZAId2dC0vo1Jpf1th_DLklKeKnnotAa5C_UKV-u</recordid><startdate>20110927</startdate><enddate>20110927</enddate><creator>Benoîte de Saporta</creator><creator>Gégout-Petit, Anne</creator><creator>Marsalle, Laurence</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20110927</creationdate><title>Parameters estimation for asymmetric bifurcating autoregressive processes with missing data</title><author>Benoîte de Saporta ; Gégout-Petit, Anne ; Marsalle, Laurence</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a510-9032c412bcd1e1bdae0c0290a5a643c6fbb1525c965c99f715b3608f5da2142b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Autoregressive processes</topic><topic>Bifurcations</topic><topic>Branching (mathematics)</topic><topic>Martingales</topic><topic>Mathematics - Probability</topic><topic>Mathematics - Statistics Theory</topic><topic>Missing data</topic><topic>Normality</topic><topic>Parameter estimation</topic><topic>Regression analysis</topic><topic>Statistics - Theory</topic><topic>Stochastic processes</topic><toplevel>online_resources</toplevel><creatorcontrib>Benoîte de Saporta</creatorcontrib><creatorcontrib>Gégout-Petit, Anne</creatorcontrib><creatorcontrib>Marsalle, Laurence</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv Statistics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Benoîte de Saporta</au><au>Gégout-Petit, Anne</au><au>Marsalle, Laurence</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Parameters estimation for asymmetric bifurcating autoregressive processes with missing data</atitle><jtitle>arXiv.org</jtitle><date>2011-09-27</date><risdate>2011</risdate><eissn>2331-8422</eissn><abstract>We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1012.2012</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2011-09 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_1012_2012 |
| source | arXiv.org; Free E- Journals |
| subjects | Autoregressive processes Bifurcations Branching (mathematics) Martingales Mathematics - Probability Mathematics - Statistics Theory Missing data Normality Parameter estimation Regression analysis Statistics - Theory Stochastic processes |
| title | Parameters estimation for asymmetric bifurcating autoregressive processes with missing data |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-11T10%3A43%3A56IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Parameters%20estimation%20for%20asymmetric%20bifurcating%20autoregressive%20processes%20with%20missing%20data&rft.jtitle=arXiv.org&rft.au=Beno%C3%AEte%20de%20Saporta&rft.date=2011-09-27&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1012.2012&rft_dat=%3Cproquest_arxiv%3E2086714660%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2086714660&rft_id=info:pmid/&rfr_iscdi=true |