The Distribution of Robust Distances
Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chi-squared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum...
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| Veröffentlicht in: | Journal of computational and graphical statistics 2005-12, Vol.14 (4), p.928-946 |
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| container_title | Journal of computational and graphical statistics |
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| creator | Hardin, Johanna Rocke, David M |
| description | Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chi-squared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes. |
| doi_str_mv | 10.1198/106186005X77685 |
| format | Article |
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For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes.</description><identifier>ISSN: 1061-8600</identifier><identifier>EISSN: 1537-2715</identifier><identifier>DOI: 10.1198/106186005X77685</identifier><language>eng</language><publisher>Alexandria: Taylor & Francis</publisher><subject>Approximation ; Asymptotic value ; Covariance ; Covariance matrices ; Degrees of freedom ; Estimators ; Graph algorithms ; Mahalanobis squared distance ; Minimum covariance determinant ; Multivariate analysis ; Outlier detection ; Outliers ; Perceptual localization ; Robust estimation ; Sampling distributions ; Statistics ; Variance analysis</subject><ispartof>Journal of computational and graphical statistics, 2005-12, Vol.14 (4), p.928-946</ispartof><rights>American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America 2005</rights><rights>Copyright 2005 American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America</rights><rights>Copyright American Statistical Association Dec 2005</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c428t-da545767baaffa94c5e4114d46cb2e0bd96352cface199c99257aef04c2a6ec23</citedby><cites>FETCH-LOGICAL-c428t-da545767baaffa94c5e4114d46cb2e0bd96352cface199c99257aef04c2a6ec23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/27594157$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/27594157$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Hardin, Johanna</creatorcontrib><creatorcontrib>Rocke, David M</creatorcontrib><title>The Distribution of Robust Distances</title><title>Journal of computational and graphical statistics</title><description>Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chi-squared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes.</description><subject>Approximation</subject><subject>Asymptotic value</subject><subject>Covariance</subject><subject>Covariance matrices</subject><subject>Degrees of freedom</subject><subject>Estimators</subject><subject>Graph algorithms</subject><subject>Mahalanobis squared distance</subject><subject>Minimum covariance determinant</subject><subject>Multivariate analysis</subject><subject>Outlier detection</subject><subject>Outliers</subject><subject>Perceptual localization</subject><subject>Robust estimation</subject><subject>Sampling distributions</subject><subject>Statistics</subject><subject>Variance analysis</subject><issn>1061-8600</issn><issn>1537-2715</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><recordid>eNp1kM1LxDAQxYMouK6ePQlFvNbNpPlovMmuX7AgyAreQpom2KXbrEmK7H9v14oHwdMM83vvDTyEzgFfA8hyBphDyTFmb0Lwkh2gCbBC5EQAOxz2geZ7fIxOYlxjjIFLMUFXq3ebLZqYQlP1qfFd5l324qs-pu-z7oyNp-jI6Tbas585Ra_3d6v5Y758fnia3y5zQ0mZ8lozygQXldbOaUkNsxSA1pSbilhc1ZIXjBinjQUpjZSECW0dpoZobg0ppuhyzN0G_9HbmNTa96EbXipSMCFowfei2SgywccYrFPb0Gx02CnAat-E-tPE4LgYHeuYfPiVE8EkBSYGfjPypnM-bPSnD22tkt61PrgwNNBEVfwX_gX7F2vG</recordid><startdate>20051201</startdate><enddate>20051201</enddate><creator>Hardin, Johanna</creator><creator>Rocke, David M</creator><general>Taylor & Francis</general><general>American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America</general><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20051201</creationdate><title>The Distribution of Robust Distances</title><author>Hardin, Johanna ; Rocke, David M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c428t-da545767baaffa94c5e4114d46cb2e0bd96352cface199c99257aef04c2a6ec23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Approximation</topic><topic>Asymptotic value</topic><topic>Covariance</topic><topic>Covariance matrices</topic><topic>Degrees of freedom</topic><topic>Estimators</topic><topic>Graph algorithms</topic><topic>Mahalanobis squared distance</topic><topic>Minimum covariance determinant</topic><topic>Multivariate analysis</topic><topic>Outlier detection</topic><topic>Outliers</topic><topic>Perceptual localization</topic><topic>Robust estimation</topic><topic>Sampling distributions</topic><topic>Statistics</topic><topic>Variance analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hardin, Johanna</creatorcontrib><creatorcontrib>Rocke, David M</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Journal of computational and graphical statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hardin, Johanna</au><au>Rocke, David M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Distribution of Robust Distances</atitle><jtitle>Journal of computational and graphical statistics</jtitle><date>2005-12-01</date><risdate>2005</risdate><volume>14</volume><issue>4</issue><spage>928</spage><epage>946</epage><pages>928-946</pages><issn>1061-8600</issn><eissn>1537-2715</eissn><abstract>Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chi-squared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes.</abstract><cop>Alexandria</cop><pub>Taylor & Francis</pub><doi>10.1198/106186005X77685</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of computational and graphical statistics, 2005-12, Vol.14 (4), p.928-946 |
| issn | 1061-8600 1537-2715 |
| language | eng |
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| source | Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| subjects | Approximation Asymptotic value Covariance Covariance matrices Degrees of freedom Estimators Graph algorithms Mahalanobis squared distance Minimum covariance determinant Multivariate analysis Outlier detection Outliers Perceptual localization Robust estimation Sampling distributions Statistics Variance analysis |
| title | The Distribution of Robust Distances |
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