Robust Maximum Association Estimators
The maximum association between two multivariate variables and is defined as the maximal value that a bivariate association measure between one-dimensional projections and can attain. Taking the Pearson correlation as projection index results in the first canonical correlation coefficient. We propos...
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Veröffentlicht in: | Journal of the American Statistical Association 2017-03, Vol.112 (517), p.436-445 |
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creator | Alfons, Andreas Croux, Christophe Filzmoser, Peter |
description | The maximum association between two multivariate variables
and
is defined as the maximal value that a bivariate association measure between one-dimensional projections
and
can attain. Taking the Pearson correlation as projection index results in the first canonical correlation coefficient. We propose to use more robust association measures, such as Spearman's or Kendall's rank correlation, or association measures derived from bivariate scatter matrices. We study the robustness of the proposed maximum association measures and the corresponding estimators of the coefficients yielding the maximum association. In the important special case of
being univariate, maximum rank correlation estimators yield regression estimators that are invariant against monotonic transformations of the response. We obtain asymptotic variances for this special case. It turns out that maximum rank correlation estimators combine good efficiency and robustness properties. Simulations and a real data example illustrate the robustness and the power for handling nonlinear relationships of these estimators. Supplementary materials for this article are available online. |
doi_str_mv | 10.1080/01621459.2016.1148609 |
format | Article |
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and
is defined as the maximal value that a bivariate association measure between one-dimensional projections
and
can attain. Taking the Pearson correlation as projection index results in the first canonical correlation coefficient. We propose to use more robust association measures, such as Spearman's or Kendall's rank correlation, or association measures derived from bivariate scatter matrices. We study the robustness of the proposed maximum association measures and the corresponding estimators of the coefficients yielding the maximum association. In the important special case of
being univariate, maximum rank correlation estimators yield regression estimators that are invariant against monotonic transformations of the response. We obtain asymptotic variances for this special case. It turns out that maximum rank correlation estimators combine good efficiency and robustness properties. Simulations and a real data example illustrate the robustness and the power for handling nonlinear relationships of these estimators. Supplementary materials for this article are available online.</description><identifier>ISSN: 0162-1459</identifier><identifier>EISSN: 1537-274X</identifier><identifier>DOI: 10.1080/01621459.2016.1148609</identifier><language>eng</language><publisher>Alexandria: Taylor & Francis</publisher><subject>Bivariate analysis ; Correlation analysis ; Correlation coefficients ; Economic models ; Estimators ; Influence function ; Materials handling ; Mathematical analysis ; Matrices ; Power ; Projection pursuit ; Projections ; Rank correlation ; Regression ; Regression analysis ; Robustness ; Statistical methods ; Statistics ; Theory and Methods</subject><ispartof>Journal of the American Statistical Association, 2017-03, Vol.112 (517), p.436-445</ispartof><rights>2017 The Author(s). Published with license by Taylor & Francis © Andreas Alfons, Christophe Croux, and Peter Filzmoser 2017</rights><rights>Copyright © 2017 American Statistical Association</rights><rights>2017 The Author(s). Published with license by Taylor & Francis; © Andreas Alfons, Christophe Croux, and Peter Filzmoser</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c440t-ca11792b22f5d9a27f9482d79a8124af81ec968199d21019f91e1d224a43b0af3</citedby><cites>FETCH-LOGICAL-c440t-ca11792b22f5d9a27f9482d79a8124af81ec968199d21019f91e1d224a43b0af3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/45027930$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/45027930$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>315,781,785,804,833,27926,27927,58019,58023,58252,58256,59649,60438</link.rule.ids></links><search><creatorcontrib>Alfons, Andreas</creatorcontrib><creatorcontrib>Croux, Christophe</creatorcontrib><creatorcontrib>Filzmoser, Peter</creatorcontrib><title>Robust Maximum Association Estimators</title><title>Journal of the American Statistical Association</title><description>The maximum association between two multivariate variables
and
is defined as the maximal value that a bivariate association measure between one-dimensional projections
and
can attain. Taking the Pearson correlation as projection index results in the first canonical correlation coefficient. We propose to use more robust association measures, such as Spearman's or Kendall's rank correlation, or association measures derived from bivariate scatter matrices. We study the robustness of the proposed maximum association measures and the corresponding estimators of the coefficients yielding the maximum association. In the important special case of
being univariate, maximum rank correlation estimators yield regression estimators that are invariant against monotonic transformations of the response. We obtain asymptotic variances for this special case. It turns out that maximum rank correlation estimators combine good efficiency and robustness properties. Simulations and a real data example illustrate the robustness and the power for handling nonlinear relationships of these estimators. Supplementary materials for this article are available online.</description><subject>Bivariate analysis</subject><subject>Correlation analysis</subject><subject>Correlation coefficients</subject><subject>Economic models</subject><subject>Estimators</subject><subject>Influence function</subject><subject>Materials handling</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Power</subject><subject>Projection pursuit</subject><subject>Projections</subject><subject>Rank correlation</subject><subject>Regression</subject><subject>Regression analysis</subject><subject>Robustness</subject><subject>Statistical methods</subject><subject>Statistics</subject><subject>Theory and Methods</subject><issn>0162-1459</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>0YH</sourceid><recordid>eNp9UE1LAzEQDaJgrf6EQkE8bs0k2Sa5WUr9gIogCt5CuruBLd1NzWTR_nuzbPXoXGbgvTdv5hEyAToDqugthTkDkesZS9MMQKg51SdkBDmXGZPi45SMek7Wk87JBeKWppJKjcjNq990GKfP9rtuuma6QPRFbWPt2-kKY93Y6ANekjNnd1hdHfuYvN-v3paP2frl4Wm5WGeFEDRmhQWQmm0Yc3mpLZNOC8VKqa0CJqxTUBV6rkDrkgEF7TRUULIECb6h1vExuR727oP_7CqMZuu70CZLwziXUgqRi8TKB1YRPGKonNmHdGg4GKCmT8T8JmL6RMwxkaSbDLotpqf-RCKnTGpOE3434HXrfGjslw-70kR72Pnggm2LGg3_3-IH0jRvFw</recordid><startdate>20170301</startdate><enddate>20170301</enddate><creator>Alfons, Andreas</creator><creator>Croux, Christophe</creator><creator>Filzmoser, Peter</creator><general>Taylor & Francis</general><general>Taylor & Francis Group,LLC</general><general>Taylor & Francis Ltd</general><scope>0YH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope><scope>K9.</scope></search><sort><creationdate>20170301</creationdate><title>Robust Maximum Association Estimators</title><author>Alfons, Andreas ; Croux, Christophe ; Filzmoser, Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c440t-ca11792b22f5d9a27f9482d79a8124af81ec968199d21019f91e1d224a43b0af3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Bivariate analysis</topic><topic>Correlation analysis</topic><topic>Correlation coefficients</topic><topic>Economic models</topic><topic>Estimators</topic><topic>Influence function</topic><topic>Materials handling</topic><topic>Mathematical analysis</topic><topic>Matrices</topic><topic>Power</topic><topic>Projection pursuit</topic><topic>Projections</topic><topic>Rank correlation</topic><topic>Regression</topic><topic>Regression analysis</topic><topic>Robustness</topic><topic>Statistical methods</topic><topic>Statistics</topic><topic>Theory and Methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alfons, Andreas</creatorcontrib><creatorcontrib>Croux, Christophe</creatorcontrib><creatorcontrib>Filzmoser, Peter</creatorcontrib><collection>Taylor & Francis (Open access)</collection><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><jtitle>Journal of the American Statistical Association</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alfons, Andreas</au><au>Croux, Christophe</au><au>Filzmoser, Peter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust Maximum Association Estimators</atitle><jtitle>Journal of the American Statistical Association</jtitle><date>2017-03-01</date><risdate>2017</risdate><volume>112</volume><issue>517</issue><spage>436</spage><epage>445</epage><pages>436-445</pages><issn>0162-1459</issn><eissn>1537-274X</eissn><abstract>The maximum association between two multivariate variables
and
is defined as the maximal value that a bivariate association measure between one-dimensional projections
and
can attain. Taking the Pearson correlation as projection index results in the first canonical correlation coefficient. We propose to use more robust association measures, such as Spearman's or Kendall's rank correlation, or association measures derived from bivariate scatter matrices. We study the robustness of the proposed maximum association measures and the corresponding estimators of the coefficients yielding the maximum association. In the important special case of
being univariate, maximum rank correlation estimators yield regression estimators that are invariant against monotonic transformations of the response. We obtain asymptotic variances for this special case. It turns out that maximum rank correlation estimators combine good efficiency and robustness properties. Simulations and a real data example illustrate the robustness and the power for handling nonlinear relationships of these estimators. Supplementary materials for this article are available online.</abstract><cop>Alexandria</cop><pub>Taylor & Francis</pub><doi>10.1080/01621459.2016.1148609</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
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source | JSTOR Mathematics and Statistics; Taylor & Francis Online; JSTOR |
subjects | Bivariate analysis Correlation analysis Correlation coefficients Economic models Estimators Influence function Materials handling Mathematical analysis Matrices Power Projection pursuit Projections Rank correlation Regression Regression analysis Robustness Statistical methods Statistics Theory and Methods |
title | Robust Maximum Association Estimators |
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