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Article: Depth functions as measures of representativeness
Title | Depth functions as measures of representativeness |
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Authors | |
Keywords | Centre-outward ordering Data depth Goodness-of-fit tests Multimodality Representativeness |
Issue Date | 2014 |
Publisher | Springer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00362/index.htm |
Citation | Statistical Papers, 2014, v. 55 n. 4, p. 1079-1105 How to Cite? |
Abstract | Data depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. Most existing depth functions emphasize a centre-outward ordering of data points, which may not provide a useful geometric representation of certain distributional features, such as multimodality, of concern to some statistical applications. Such inadequacy motivates us to develop a device for ranking data points according to their “representativeness” rather than “centrality” with respect to an underlying distribution of interest. Derived essentially from 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, depth functions derived from goodness-of-fit tests also extend naturally to provide depth values for subsets of data points, a concept new to the data-depth literature. |
Persistent Identifier | http://hdl.handle.net/10722/189450 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 0.659 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Dong, Y | - |
dc.contributor.author | Lee, SMS | - |
dc.date.accessioned | 2013-09-17T14:41:47Z | - |
dc.date.available | 2013-09-17T14:41:47Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Statistical Papers, 2014, v. 55 n. 4, p. 1079-1105 | - |
dc.identifier.issn | 0932-5026 | - |
dc.identifier.uri | http://hdl.handle.net/10722/189450 | - |
dc.description.abstract | Data depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. Most existing depth functions emphasize a centre-outward ordering of data points, which may not provide a useful geometric representation of certain distributional features, such as multimodality, of concern to some statistical applications. Such inadequacy motivates us to develop a device for ranking data points according to their “representativeness” rather than “centrality” with respect to an underlying distribution of interest. Derived essentially from 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, depth functions derived from goodness-of-fit tests also extend naturally to provide depth values for subsets of data points, a concept new to the data-depth literature. | - |
dc.language | eng | - |
dc.publisher | Springer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00362/index.htm | - |
dc.relation.ispartof | Statistical Papers | - |
dc.rights | The final publication is available at Springer via http://dx.doi.org/10.1007/s00362-013-0555-5 | - |
dc.subject | Centre-outward ordering | - |
dc.subject | Data depth | - |
dc.subject | Goodness-of-fit tests | - |
dc.subject | Multimodality | - |
dc.subject | Representativeness | - |
dc.title | Depth functions as measures of representativeness | - |
dc.type | Article | - |
dc.identifier.email | Lee, SMS: smslee@hku.hk | - |
dc.identifier.authority | Lee, SMS=rp00726 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1007/s00362-013-0555-5 | - |
dc.identifier.scopus | eid_2-s2.0-84908498047 | - |
dc.identifier.hkuros | 223126 | - |
dc.identifier.volume | 55 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 1079 | - |
dc.identifier.epage | 1105 | - |
dc.identifier.isi | WOS:000343046200011 | - |
dc.publisher.place | Germany | - |
dc.identifier.issnl | 0932-5026 | - |