Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs
Test of independence between random vectors X and Y is an essential task in statistical inference. One type of testing methods is based on the minimal spanning tree of variables X and Y . The main idea is to generate the minimal spanning tree for one random vector X , and for each edges in minimal s...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2022, Vol.38 (4), p.662-682 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Liu, Jia Min Li, Gao Rong Zhang, Jian Qiang Xu, Wang Li |
| description | Test of independence between random vectors
X
and
Y
is an essential task in statistical inference. One type of testing methods is based on the minimal spanning tree of variables
X
and
Y
. The main idea is to generate the minimal spanning tree for one random vector
X
, and for each edges in minimal spanning tree, the corresponding rank number can be calculated based on another random vector
Y
. The resulting test statistics are constructed by these rank numbers. However, the existed statistics are not symmetrical tests about the random vectors
X
and
Y
such that the power performance from minimal spanning tree of
X
is not the same as that from minimal spanning tree of
Y
. In addition, the conclusion from minimal spanning tree of
X
might conflict with that from minimal spanning tree of
Y
. In order to solve these problems, we propose several symmetrical independence tests for
X
and
Y.
The exact distributions of test statistics are investigated when the sample size is small. Also, we study the asymptotic properties of the statistics. A permutation method is introduced for getting critical values of the statistics. Compared with the existing methods, our proposed methods are more efficient demonstrated by numerical analysis. |
| doi_str_mv | 10.1007/s10114-022-0045-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2653809114</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2653809114</sourcerecordid><originalsourceid>FETCH-LOGICAL-c1136-c9124de4f7bb2bd7f6b03bf99918cdaf3dcbce983d678ae8998fd425376778833</originalsourceid><addsrcrecordid>eNp1kE1LAzEYhIMoWKs_wFvAczTZ7ObjWKrWQkHQVY9hNx92S3ezJltK_70pW_Dk5Z33MDMMDwC3BN8TjPlDJJiQHOEsQxjnBWJnYEJyKhFnhJ-fflEQdgmuYtxgXBQSswn4ej-0rR1Co6stXHbG9jadTltY2jhE6HyA5d7Dt6ozvoWfVg8-RLhvhjWchboZQhUO8LFpbRcb36WSRaj6dbwGF67aRntz0in4eH4q5y9o9bpYzmcrpAmhDGlJstzY3PG6zmrDHasxrZ2UkghtKkeNrrWVghrGRWWFlMKZPCsoZ5wLQekU3I29ffA_uzRZbfwupB1RZaygAsuEJbnI6NLBxxisU31o2rRcEayO_NTITyV-6shPsZTJxkxM3u7bhr_m_0O_9-JzMw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2653809114</pqid></control><display><type>article</type><title>Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs</title><source>Alma/SFX Local Collection</source><source>SpringerLink Journals - AutoHoldings</source><creator>Liu, Jia Min ; Li, Gao Rong ; Zhang, Jian Qiang ; Xu, Wang Li</creator><creatorcontrib>Liu, Jia Min ; Li, Gao Rong ; Zhang, Jian Qiang ; Xu, Wang Li</creatorcontrib><description>Test of independence between random vectors
X
and
Y
is an essential task in statistical inference. One type of testing methods is based on the minimal spanning tree of variables
X
and
Y
. The main idea is to generate the minimal spanning tree for one random vector
X
, and for each edges in minimal spanning tree, the corresponding rank number can be calculated based on another random vector
Y
. The resulting test statistics are constructed by these rank numbers. However, the existed statistics are not symmetrical tests about the random vectors
X
and
Y
such that the power performance from minimal spanning tree of
X
is not the same as that from minimal spanning tree of
Y
. In addition, the conclusion from minimal spanning tree of
X
might conflict with that from minimal spanning tree of
Y
. In order to solve these problems, we propose several symmetrical independence tests for
X
and
Y.
The exact distributions of test statistics are investigated when the sample size is small. Also, we study the asymptotic properties of the statistics. A permutation method is introduced for getting critical values of the statistics. Compared with the existing methods, our proposed methods are more efficient demonstrated by numerical analysis.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-022-0045-6</identifier><language>eng</language><publisher>Beijing: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</publisher><subject>Asymptotic properties ; Mathematics ; Mathematics and Statistics ; Numerical analysis ; Permutations ; Statistical inference ; Statistical tests ; Statistics</subject><ispartof>Acta mathematica Sinica. English series, 2022, Vol.38 (4), p.662-682</ispartof><rights>Springer-Verlag GmbH Germany & The Editorial Office of AMS 2022</rights><rights>Springer-Verlag GmbH Germany & The Editorial Office of AMS 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1136-c9124de4f7bb2bd7f6b03bf99918cdaf3dcbce983d678ae8998fd425376778833</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10114-022-0045-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10114-022-0045-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Liu, Jia Min</creatorcontrib><creatorcontrib>Li, Gao Rong</creatorcontrib><creatorcontrib>Zhang, Jian Qiang</creatorcontrib><creatorcontrib>Xu, Wang Li</creatorcontrib><title>Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs</title><title>Acta mathematica Sinica. English series</title><addtitle>Acta. Math. Sin.-English Ser</addtitle><description>Test of independence between random vectors
X
and
Y
is an essential task in statistical inference. One type of testing methods is based on the minimal spanning tree of variables
X
and
Y
. The main idea is to generate the minimal spanning tree for one random vector
X
, and for each edges in minimal spanning tree, the corresponding rank number can be calculated based on another random vector
Y
. The resulting test statistics are constructed by these rank numbers. However, the existed statistics are not symmetrical tests about the random vectors
X
and
Y
such that the power performance from minimal spanning tree of
X
is not the same as that from minimal spanning tree of
Y
. In addition, the conclusion from minimal spanning tree of
X
might conflict with that from minimal spanning tree of
Y
. In order to solve these problems, we propose several symmetrical independence tests for
X
and
Y.
The exact distributions of test statistics are investigated when the sample size is small. Also, we study the asymptotic properties of the statistics. A permutation method is introduced for getting critical values of the statistics. Compared with the existing methods, our proposed methods are more efficient demonstrated by numerical analysis.</description><subject>Asymptotic properties</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical analysis</subject><subject>Permutations</subject><subject>Statistical inference</subject><subject>Statistical tests</subject><subject>Statistics</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEYhIMoWKs_wFvAczTZ7ObjWKrWQkHQVY9hNx92S3ezJltK_70pW_Dk5Z33MDMMDwC3BN8TjPlDJJiQHOEsQxjnBWJnYEJyKhFnhJ-fflEQdgmuYtxgXBQSswn4ej-0rR1Co6stXHbG9jadTltY2jhE6HyA5d7Dt6ozvoWfVg8-RLhvhjWchboZQhUO8LFpbRcb36WSRaj6dbwGF67aRntz0in4eH4q5y9o9bpYzmcrpAmhDGlJstzY3PG6zmrDHasxrZ2UkghtKkeNrrWVghrGRWWFlMKZPCsoZ5wLQekU3I29ffA_uzRZbfwupB1RZaygAsuEJbnI6NLBxxisU31o2rRcEayO_NTITyV-6shPsZTJxkxM3u7bhr_m_0O_9-JzMw</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Liu, Jia Min</creator><creator>Li, Gao Rong</creator><creator>Zhang, Jian Qiang</creator><creator>Xu, Wang Li</creator><general>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2022</creationdate><title>Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs</title><author>Liu, Jia Min ; Li, Gao Rong ; Zhang, Jian Qiang ; Xu, Wang Li</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1136-c9124de4f7bb2bd7f6b03bf99918cdaf3dcbce983d678ae8998fd425376778833</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Asymptotic properties</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical analysis</topic><topic>Permutations</topic><topic>Statistical inference</topic><topic>Statistical tests</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Jia Min</creatorcontrib><creatorcontrib>Li, Gao Rong</creatorcontrib><creatorcontrib>Zhang, Jian Qiang</creatorcontrib><creatorcontrib>Xu, Wang Li</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Acta mathematica Sinica. English series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Jia Min</au><au>Li, Gao Rong</au><au>Zhang, Jian Qiang</au><au>Xu, Wang Li</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs</atitle><jtitle>Acta mathematica Sinica. English series</jtitle><stitle>Acta. Math. Sin.-English Ser</stitle><date>2022</date><risdate>2022</risdate><volume>38</volume><issue>4</issue><spage>662</spage><epage>682</epage><pages>662-682</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>Test of independence between random vectors
X
and
Y
is an essential task in statistical inference. One type of testing methods is based on the minimal spanning tree of variables
X
and
Y
. The main idea is to generate the minimal spanning tree for one random vector
X
, and for each edges in minimal spanning tree, the corresponding rank number can be calculated based on another random vector
Y
. The resulting test statistics are constructed by these rank numbers. However, the existed statistics are not symmetrical tests about the random vectors
X
and
Y
such that the power performance from minimal spanning tree of
X
is not the same as that from minimal spanning tree of
Y
. In addition, the conclusion from minimal spanning tree of
X
might conflict with that from minimal spanning tree of
Y
. In order to solve these problems, we propose several symmetrical independence tests for
X
and
Y.
The exact distributions of test statistics are investigated when the sample size is small. Also, we study the asymptotic properties of the statistics. A permutation method is introduced for getting critical values of the statistics. Compared with the existing methods, our proposed methods are more efficient demonstrated by numerical analysis.</abstract><cop>Beijing</cop><pub>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</pub><doi>10.1007/s10114-022-0045-6</doi><tpages>21</tpages></addata></record> |
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| language | eng |
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| subjects | Asymptotic properties Mathematics Mathematics and Statistics Numerical analysis Permutations Statistical inference Statistical tests Statistics |
| title | Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs |
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