Asymptotic distribution for the proportional covariance model
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in three steps. First, the asymptotic distribution of the maxim...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Kim, Myung Geun |
| description | Asymptotic distribution for the proportional covariance model under
multivariate normal distributions is derived. To this end, the parametrization
of the common covariance matrix by its Cholesky root is adopted. The
derivations are made in three steps. First, the asymptotic distribution of the
maximum likelihood estimators of the proportionality coefficients and the
Cholesky inverse root of the common covariance matrix is derived by finding the
information matrix and its inverse. Next, the asymptotic distributions for the
case of the Cholesky root of the common covariance matrix and finally for the
case of the common covariance matrix itself are derived using the multivariate
$\delta$-method. As an application of the asymptotic distribution derived here,
a hypothesis for homogeneity of covariance matrices is considered. |
| doi_str_mv | 10.48550/arxiv.2103.11280 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2103_11280</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2103_11280</sourcerecordid><originalsourceid>FETCH-LOGICAL-a670-116862d7832ce3c0f077048b8db04cb5da17d7a5dd041b5a4b78a1824521df213</originalsourceid><addsrcrecordid>eNotj71qwzAURrV0KGkeoFP1Anbv1Y-lpUMIbVoIdMlurn5MBXZkZDU0bx-SdDrwDYfvMPaM0CqrNbxS-UunViDIFlFYeGRvm-U8zTXX5HlISy3J_daUj3zIhdefyOeS51yuE43c5xOVREcf-ZRDHJ_Yw0DjEtf_XLHDx_th-9nsv3df282-oc5Ag9jZTgRjpfBRehjAGFDW2eBAeacDoQmGdAig0GlSzlhCK5QWGAaBcsVe7trb_34uaaJy7q8d_a1DXgCnXEMV</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Asymptotic distribution for the proportional covariance model</title><source>arXiv.org</source><creator>Kim, Myung Geun</creator><creatorcontrib>Kim, Myung Geun</creatorcontrib><description>Asymptotic distribution for the proportional covariance model under
multivariate normal distributions is derived. To this end, the parametrization
of the common covariance matrix by its Cholesky root is adopted. The
derivations are made in three steps. First, the asymptotic distribution of the
maximum likelihood estimators of the proportionality coefficients and the
Cholesky inverse root of the common covariance matrix is derived by finding the
information matrix and its inverse. Next, the asymptotic distributions for the
case of the Cholesky root of the common covariance matrix and finally for the
case of the common covariance matrix itself are derived using the multivariate
$\delta$-method. As an application of the asymptotic distribution derived here,
a hypothesis for homogeneity of covariance matrices is considered.</description><identifier>DOI: 10.48550/arxiv.2103.11280</identifier><language>eng</language><subject>Mathematics - Statistics Theory ; Statistics - Theory</subject><creationdate>2021-03</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2103.11280$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2103.11280$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kim, Myung Geun</creatorcontrib><title>Asymptotic distribution for the proportional covariance model</title><description>Asymptotic distribution for the proportional covariance model under
multivariate normal distributions is derived. To this end, the parametrization
of the common covariance matrix by its Cholesky root is adopted. The
derivations are made in three steps. First, the asymptotic distribution of the
maximum likelihood estimators of the proportionality coefficients and the
Cholesky inverse root of the common covariance matrix is derived by finding the
information matrix and its inverse. Next, the asymptotic distributions for the
case of the Cholesky root of the common covariance matrix and finally for the
case of the common covariance matrix itself are derived using the multivariate
$\delta$-method. As an application of the asymptotic distribution derived here,
a hypothesis for homogeneity of covariance matrices is considered.</description><subject>Mathematics - Statistics Theory</subject><subject>Statistics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj71qwzAURrV0KGkeoFP1Anbv1Y-lpUMIbVoIdMlurn5MBXZkZDU0bx-SdDrwDYfvMPaM0CqrNbxS-UunViDIFlFYeGRvm-U8zTXX5HlISy3J_daUj3zIhdefyOeS51yuE43c5xOVREcf-ZRDHJ_Yw0DjEtf_XLHDx_th-9nsv3df282-oc5Ag9jZTgRjpfBRehjAGFDW2eBAeacDoQmGdAig0GlSzlhCK5QWGAaBcsVe7trb_34uaaJy7q8d_a1DXgCnXEMV</recordid><startdate>20210320</startdate><enddate>20210320</enddate><creator>Kim, Myung Geun</creator><scope>AKZ</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20210320</creationdate><title>Asymptotic distribution for the proportional covariance model</title><author>Kim, Myung Geun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-116862d7832ce3c0f077048b8db04cb5da17d7a5dd041b5a4b78a1824521df213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Statistics Theory</topic><topic>Statistics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Kim, Myung Geun</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv Statistics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kim, Myung Geun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic distribution for the proportional covariance model</atitle><date>2021-03-20</date><risdate>2021</risdate><abstract>Asymptotic distribution for the proportional covariance model under
multivariate normal distributions is derived. To this end, the parametrization
of the common covariance matrix by its Cholesky root is adopted. The
derivations are made in three steps. First, the asymptotic distribution of the
maximum likelihood estimators of the proportionality coefficients and the
Cholesky inverse root of the common covariance matrix is derived by finding the
information matrix and its inverse. Next, the asymptotic distributions for the
case of the Cholesky root of the common covariance matrix and finally for the
case of the common covariance matrix itself are derived using the multivariate
$\delta$-method. As an application of the asymptotic distribution derived here,
a hypothesis for homogeneity of covariance matrices is considered.</abstract><doi>10.48550/arxiv.2103.11280</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2103.11280 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2103_11280 |
| source | arXiv.org |
| subjects | Mathematics - Statistics Theory Statistics - Theory |
| title | Asymptotic distribution for the proportional covariance model |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T03%3A27%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Asymptotic%20distribution%20for%20the%20proportional%20covariance%20model&rft.au=Kim,%20Myung%20Geun&rft.date=2021-03-20&rft_id=info:doi/10.48550/arxiv.2103.11280&rft_dat=%3Carxiv_GOX%3E2103_11280%3C/arxiv_GOX%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 |