Optimal second-order product probability bounds
Let P(c) = P(X 1 ≦ c 1, · ··, Xp ≦ cp ) for a random vector (X 1, · ··, Xp ). Bounds are considered of the form where T is a spanning tree corresponding to the bivariate probability structure and di is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main res...
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| Veröffentlicht in: | Journal of applied probability 1993-09, Vol.30 (3), p.675-691 |
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| container_end_page | 691 |
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| container_start_page | 675 |
| container_title | Journal of applied probability |
| container_volume | 30 |
| creator | Block, Henry W. Costigan, Timothy M. Sampson, Allan R. |
| description | Let P(c) = P(X
1 ≦ c
1, · ··, Xp
≦ cp
) for a random vector (X
1, · ··, Xp
). Bounds are considered of the form
where T is a spanning tree corresponding to the bivariate probability structure and di
is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main result is that alwayṡ dominates certain second-order Bonferroni bounds. Conditions on the covariance matrix of a N(0,Σ) distribution are given so that this bound applies, and various applications are given. |
| doi_str_mv | 10.2307/3214774 |
| format | Article |
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1 ≦ c
1, · ··, Xp
≦ cp
) for a random vector (X
1, · ··, Xp
). Bounds are considered of the form
where T is a spanning tree corresponding to the bivariate probability structure and di
is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main result is that alwayṡ dominates certain second-order Bonferroni bounds. Conditions on the covariance matrix of a N(0,Σ) distribution are given so that this bound applies, and various applications are given.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.2307/3214774</identifier><identifier>CODEN: JPRBAM</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Algorithms ; Applications ; Exact sciences and technology ; Mathematical models ; Mathematics ; Multivariate analysis ; Probability ; Probability and statistics ; Regression analysis ; Research Papers ; Sciences and techniques of general use ; Statistics ; Studies ; Theory</subject><ispartof>Journal of applied probability, 1993-09, Vol.30 (3), p.675-691</ispartof><rights>Copyright © Applied Probability Trust 1993</rights><rights>Copyright 1993 Applied Probability Trust</rights><rights>1994 INIST-CNRS</rights><rights>Copyright Applied Probability Trust Sep 1993</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c274t-7140fa81d156baa6b2bc037e328ed7786a3f8aff1b3ac2a0f64ee64eb993f5403</citedby><cites>FETCH-LOGICAL-c274t-7140fa81d156baa6b2bc037e328ed7786a3f8aff1b3ac2a0f64ee64eb993f5403</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/3214774$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/3214774$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27923,27924,58016,58020,58249,58253</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3811767$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Block, Henry W.</creatorcontrib><creatorcontrib>Costigan, Timothy M.</creatorcontrib><creatorcontrib>Sampson, Allan R.</creatorcontrib><title>Optimal second-order product probability bounds</title><title>Journal of applied probability</title><addtitle>Journal of Applied Probability</addtitle><description>Let P(c) = P(X
1 ≦ c
1, · ··, Xp
≦ cp
) for a random vector (X
1, · ··, Xp
). Bounds are considered of the form
where T is a spanning tree corresponding to the bivariate probability structure and di
is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main result is that alwayṡ dominates certain second-order Bonferroni bounds. Conditions on the covariance matrix of a N(0,Σ) distribution are given so that this bound applies, and various applications are given.</description><subject>Algorithms</subject><subject>Applications</subject><subject>Exact sciences and technology</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Multivariate analysis</subject><subject>Probability</subject><subject>Probability and statistics</subject><subject>Regression analysis</subject><subject>Research Papers</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><subject>Studies</subject><subject>Theory</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLw0AUhQdRsFbxLxQRxEXsnUcyyVJKfUChG12HOy9JSTN1Jln03zulwYILF_eezcc59x5Cbik8MQ5yzhkVUoozMkmaZwVIdk4mAIxmVdqX5CrGDQAVeSUnZL7e9c0W21m02ncm88HYMNsFbwbdH1Shatqm38-UHzoTr8mFwzbam1Gn5PNl-bF4y1br1_fF8yrTTIo-k1SAw5IamhcKsVBMaeDSclZaI2VZIHclOkcVR80QXCGsTaOqirtcAJ-Su6NvOuF7sLGvN34IXYqsGRcVUAYiQQ9HSAcfY7Cu3oX0TNjXFOpDGfVYRiLvRzuMGlsXsNNN_MV5Saks5AnbxN6Hf9wex1zcqtCYL3u67i_7A94NdP0</recordid><startdate>19930901</startdate><enddate>19930901</enddate><creator>Block, Henry W.</creator><creator>Costigan, Timothy M.</creator><creator>Sampson, Allan R.</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19930901</creationdate><title>Optimal second-order product probability bounds</title><author>Block, Henry W. ; Costigan, Timothy M. ; Sampson, Allan R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c274t-7140fa81d156baa6b2bc037e328ed7786a3f8aff1b3ac2a0f64ee64eb993f5403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><topic>Algorithms</topic><topic>Applications</topic><topic>Exact sciences and technology</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Multivariate analysis</topic><topic>Probability</topic><topic>Probability and statistics</topic><topic>Regression analysis</topic><topic>Research Papers</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>Studies</topic><topic>Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Block, Henry W.</creatorcontrib><creatorcontrib>Costigan, Timothy M.</creatorcontrib><creatorcontrib>Sampson, Allan R.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</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>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Block, Henry W.</au><au>Costigan, Timothy M.</au><au>Sampson, Allan R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal second-order product probability bounds</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>1993-09-01</date><risdate>1993</risdate><volume>30</volume><issue>3</issue><spage>675</spage><epage>691</epage><pages>675-691</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><coden>JPRBAM</coden><abstract>Let P(c) = P(X
1 ≦ c
1, · ··, Xp
≦ cp
) for a random vector (X
1, · ··, Xp
). Bounds are considered of the form
where T is a spanning tree corresponding to the bivariate probability structure and di
is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main result is that alwayṡ dominates certain second-order Bonferroni bounds. Conditions on the covariance matrix of a N(0,Σ) distribution are given so that this bound applies, and various applications are given.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.2307/3214774</doi><tpages>17</tpages></addata></record> |
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| ispartof | Journal of applied probability, 1993-09, Vol.30 (3), p.675-691 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_proquest_journals_234901204 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Algorithms Applications Exact sciences and technology Mathematical models Mathematics Multivariate analysis Probability Probability and statistics Regression analysis Research Papers Sciences and techniques of general use Statistics Studies Theory |
| title | Optimal second-order product probability bounds |
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