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Conference Paper: On a new class of data depths for measuring representativeness

TitleOn a new class of data depths for measuring representativeness
Authors
KeywordsCentre-outward ordering
Classification
Data depth
Goodness-of-fit tests
Interpoint distance
Multimodality
Representativeness
Issue Date2013
PublisherInternational Association for Statistical Computing.
Citation
The Joint Meeting of the IASC Satellite Conference and the 8th Conference of the Asian Regional Section of the IASC, Yonsei University, Seoul, Korea, 21-23 August 2013. In Conference Proceedings, 2013, p. 23-28 How to Cite?
AbstractData depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. The conventional notion of a depth function emphasizes a centre-outward ordering of data points. While useful for certain statistical applications, such emphasis has rendered most classical data depths insensitive to some distributional features, such as multimodality, of concern to other statistical applications. To get around the problem we introduce a new notion of data depth which seeks to rank data points according to their representativeness, rather than centrality, with respect to an underlying distribution of interest. We propose a general device for defining such depth functions, based essentially on a choice of goodness-of-fit test statistic. Our device calls for a new interpretation of depth more akin to the concept of density than location. It copes particularly well with multivariate data exhibiting multimodality. In addition to providing depth values for individual data points, the new class of depth functions derived from goodness-of-fit tests also extends naturally to provide depth values for subsets of data points, a concept new to the data-depth literature. Applications of the new depth functions are demonstrated with both simulated and real data.
DescriptionTheme: Big Data and Statistical Computing
Session SS1R1 - Data Depth
Persistent Identifierhttp://hdl.handle.net/10722/190247

 

DC FieldValueLanguage
dc.contributor.authorLee, SMSen_US
dc.date.accessioned2013-09-17T15:16:30Z-
dc.date.available2013-09-17T15:16:30Z-
dc.date.issued2013en_US
dc.identifier.citationThe Joint Meeting of the IASC Satellite Conference and the 8th Conference of the Asian Regional Section of the IASC, Yonsei University, Seoul, Korea, 21-23 August 2013. In Conference Proceedings, 2013, p. 23-28en_US
dc.identifier.urihttp://hdl.handle.net/10722/190247-
dc.descriptionTheme: Big Data and Statistical Computing-
dc.descriptionSession SS1R1 - Data Depth-
dc.description.abstractData depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. The conventional notion of a depth function emphasizes a centre-outward ordering of data points. While useful for certain statistical applications, such emphasis has rendered most classical data depths insensitive to some distributional features, such as multimodality, of concern to other statistical applications. To get around the problem we introduce a new notion of data depth which seeks to rank data points according to their representativeness, rather than centrality, with respect to an underlying distribution of interest. We propose a general device for defining such depth functions, based essentially on a choice of goodness-of-fit test statistic. Our device calls for a new interpretation of depth more akin to the concept of density than location. It copes particularly well with multivariate data exhibiting multimodality. In addition to providing depth values for individual data points, the new class of depth functions derived from goodness-of-fit tests also extends naturally to provide depth values for subsets of data points, a concept new to the data-depth literature. Applications of the new depth functions are demonstrated with both simulated and real data.-
dc.languageengen_US
dc.publisherInternational Association for Statistical Computing.-
dc.relation.ispartofProceedings of IASC Satellite Conference for the 59th ISI WSC & the 8th Conference of IASC-ARSen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectCentre-outward ordering-
dc.subjectClassification-
dc.subjectData depth-
dc.subjectGoodness-of-fit tests-
dc.subjectInterpoint distance-
dc.subjectMultimodality-
dc.subjectRepresentativeness-
dc.titleOn a new class of data depths for measuring representativenessen_US
dc.typeConference_Paperen_US
dc.identifier.emailLee, SMS: smslee@hku.hken_US
dc.identifier.authorityLee, SMS=rp00726en_US
dc.description.naturepublished_or_final_version-
dc.identifier.hkuros223130en_US
dc.identifier.spage23en_US
dc.identifier.epage28en_US
dc.publisher.placeKorea-

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