General Notions of Statistical Depth Function
Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack th...
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| Veröffentlicht in: | The Annals of statistics 2000-04, Vol.28 (2), p.461-482 |
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| container_title | The Annals of statistics |
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| creator | Zuo, Yijun Serfling, Robert |
| description | Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deepest point, and vanishing at infinity. This provides a more systematic basis for selection of a depth function. In particular, from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors. |
| doi_str_mv | 10.1214/aos/1016218226 |
| format | Article |
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In particular, from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors.</description><subject>62G20</subject><subject>62H05</subject><subject>Convexity</subject><subject>Covariance matrices</subject><subject>Data Depth</subject><subject>Datasets</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>halfspace depth</subject><subject>Inference</subject><subject>Infinity</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Maximality</subject><subject>Multivariate analysis</subject><subject>multivariate symmetry</subject><subject>Nonparametric inference</subject><subject>Probability and statistics</subject><subject>Random sampling</subject><subject>Sciences and techniques of general use</subject><subject>simplicial depth</subject><subject>Statistical depth functions</subject><subject>Statistical theories</subject><subject>Statistics</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2000</creationdate><recordtype>article</recordtype><recordid>eNplULtOwzAUtRBIlMLKxJCBNa2vX7E3UGkLUgUDdI4cxxauSlzZ7sDfk6pROzAd6byuzkXoHvAECLCpDmkKGAQBSYi4QCMCQpZSCXGJRhgrXHIq2DW6SWmDMeaK0REql7azUW-L95B96FIRXPGZdfYpe9PTL3aXv4vFvjMH-RZdOb1N9m7AMVov5l-z13L1sXybPa9KwzjOJRDdskY0jINzXDVSadtIYytjsHWsbVomGLdYKgvEKiqlJACYM02hIi2nY_R07N3FsLEm273Z-rbeRf-j428dtK9n69XADtDPr8_z-4rJscLEkFK07pQGXB_-9T_wONzUqV_uou6MT-fU4XkV7W0PR9sm5RBPMhEVw7Sif7g4c-E</recordid><startdate>20000401</startdate><enddate>20000401</enddate><creator>Zuo, Yijun</creator><creator>Serfling, Robert</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20000401</creationdate><title>General Notions of Statistical Depth Function</title><author>Zuo, Yijun ; Serfling, Robert</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c450t-12ad4b6b451ff59b89aeb8ce7cc0ef4dbd4645e089e12e93888211054a3172d53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2000</creationdate><topic>62G20</topic><topic>62H05</topic><topic>Convexity</topic><topic>Covariance matrices</topic><topic>Data Depth</topic><topic>Datasets</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>halfspace depth</topic><topic>Inference</topic><topic>Infinity</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Maximality</topic><topic>Multivariate analysis</topic><topic>multivariate symmetry</topic><topic>Nonparametric inference</topic><topic>Probability and statistics</topic><topic>Random sampling</topic><topic>Sciences and techniques of general use</topic><topic>simplicial depth</topic><topic>Statistical depth functions</topic><topic>Statistical theories</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zuo, Yijun</creatorcontrib><creatorcontrib>Serfling, Robert</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zuo, Yijun</au><au>Serfling, Robert</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>General Notions of Statistical Depth Function</atitle><jtitle>The Annals of statistics</jtitle><date>2000-04-01</date><risdate>2000</risdate><volume>28</volume><issue>2</issue><spage>461</spage><epage>482</epage><pages>461-482</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deepest point, and vanishing at infinity. This provides a more systematic basis for selection of a depth function. In particular, from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors.</abstract><cop>Hayward, CA</cop><pub>Institute of Mathematical Statistics</pub><doi>10.1214/aos/1016218226</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 62G20 62H05 Convexity Covariance matrices Data Depth Datasets Estimators Exact sciences and technology halfspace depth Inference Infinity Mathematical functions Mathematics Maximality Multivariate analysis multivariate symmetry Nonparametric inference Probability and statistics Random sampling Sciences and techniques of general use simplicial depth Statistical depth functions Statistical theories Statistics |
| title | General Notions of Statistical Depth Function |
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