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Conference Paper: On a new class of data depths for measuring representativeness
Title | On a new class of data depths for measuring representativeness |
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Authors | |
Keywords | Centre-outward ordering Classification Data depth Goodness-of-fit tests Interpoint distance Multimodality Representativeness |
Issue Date | 2013 |
Publisher | International 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? |
Abstract | Data 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. |
Description | Theme: Big Data and Statistical Computing Session SS1R1 - Data Depth |
Persistent Identifier | http://hdl.handle.net/10722/190247 |
DC Field | Value | Language |
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dc.contributor.author | Lee, SMS | en_US |
dc.date.accessioned | 2013-09-17T15:16:30Z | - |
dc.date.available | 2013-09-17T15:16:30Z | - |
dc.date.issued | 2013 | en_US |
dc.identifier.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 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/190247 | - |
dc.description | Theme: Big Data and Statistical Computing | - |
dc.description | Session SS1R1 - Data Depth | - |
dc.description.abstract | Data 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.language | eng | en_US |
dc.publisher | International Association for Statistical Computing. | - |
dc.relation.ispartof | Proceedings of IASC Satellite Conference for the 59th ISI WSC & the 8th Conference of IASC-ARS | en_US |
dc.subject | Centre-outward ordering | - |
dc.subject | Classification | - |
dc.subject | Data depth | - |
dc.subject | Goodness-of-fit tests | - |
dc.subject | Interpoint distance | - |
dc.subject | Multimodality | - |
dc.subject | Representativeness | - |
dc.title | On a new class of data depths for measuring representativeness | en_US |
dc.type | Conference_Paper | en_US |
dc.identifier.email | Lee, SMS: smslee@hku.hk | en_US |
dc.identifier.authority | Lee, SMS=rp00726 | en_US |
dc.description.nature | published_or_final_version | - |
dc.identifier.hkuros | 223130 | en_US |
dc.identifier.spage | 23 | en_US |
dc.identifier.epage | 28 | en_US |
dc.publisher.place | Korea | - |