Affine Invariant Multivariate One-Sample Sign Tests
Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable c...
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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1994-01, Vol.56 (1), p.221-234 |
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| container_title | Journal of the Royal Statistical Society. Series B, Methodological |
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| creator | Hettmansperger, Thomas P. Nyblom, Jukka Oja, Hannu |
| description | Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies of the proposed test and the Oja multivariate median are given. Lower bounds for the efficiencies of the new test (and the Randles test) relative to the classical Hotelling test are established for elliptic alternatives and for unimodal elliptic alternatives. Relative efficiencies under multivariate t-distributions are also tabulated. The theory is illustrated by a simple example. |
| doi_str_mv | 10.1111/j.2517-6161.1994.tb01973.x |
| format | Article |
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In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies of the proposed test and the Oja multivariate median are given. Lower bounds for the efficiencies of the new test (and the Randles test) relative to the classical Hotelling test are established for elliptic alternatives and for unimodal elliptic alternatives. Relative efficiencies under multivariate t-distributions are also tabulated. 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Series B, Methodological</title><description>Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies of the proposed test and the Oja multivariate median are given. Lower bounds for the efficiencies of the new test (and the Randles test) relative to the classical Hotelling test are established for elliptic alternatives and for unimodal elliptic alternatives. Relative efficiencies under multivariate t-distributions are also tabulated. The theory is illustrated by a simple example.</description><subject>asymptotic efficiency</subject><subject>blumen's test</subject><subject>Covariance matrices</subject><subject>Exact sciences and technology</subject><subject>Hyperplanes</subject><subject>location</subject><subject>Mathematical functions</subject><subject>Mathematical vectors</subject><subject>Mathematics</subject><subject>Nonparametric inference</subject><subject>Null hypothesis</subject><subject>Objective functions</subject><subject>oja median</subject><subject>one‐sample problem</subject><subject>P values</subject><subject>permutation test</subject><subject>Probability and statistics</subject><subject>randles's test</subject><subject>Random sampling</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><subject>T distribution</subject><issn>0035-9246</issn><issn>1369-7412</issn><issn>2517-6161</issn><issn>1467-9868</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1994</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><recordid>eNqVkE9PwyAYh4nRxDn9Bh4a9doKvJQOb3PxzxLNEjvPhLZg2nTthE63by9dl93lAoQfz-_Ng9ANwRHx676KaEySkBNOIiIEi7oME5FAtD1Bo-PTKRphDHEoKOPn6MK5CmNMgMEIwdSYstHBvPlRtlRNF7xv6q7cXzodLBodpmq1rnWQll9NsNSuc5fozKja6avDPkafz0_L2Wv4tniZz6ZvYQ5UQKiZ4hOGKSuoyiGLQeRC5QpirjnNYlrwGNPC-HEpy4gyepKZhAlCVAGKFRjG6Hbgrm37vfHNsmo3tvGVkgCmIhE46VMPQyq3rXNWG7m25UrZnSRY9pJkJXsTsjche0nyIElu_ee7Q4VyuaqNVU1euiOBUe6HnPjYdIj9lrXe_aNAfqTp4_7sGdcDo3Jda48MCoxjRuAPycmD-A</recordid><startdate>19940101</startdate><enddate>19940101</enddate><creator>Hettmansperger, Thomas P.</creator><creator>Nyblom, Jukka</creator><creator>Oja, Hannu</creator><general>Blackwell Publishers</general><general>Royal Statistical Society</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>HGTKA</scope><scope>JILTI</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope></search><sort><creationdate>19940101</creationdate><title>Affine Invariant Multivariate One-Sample Sign Tests</title><author>Hettmansperger, Thomas P. ; Nyblom, Jukka ; Oja, Hannu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3293-e4a684024d2ac3b539c9aca356e62b52d6502df19724b1afe8bf74911ad3a4d03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1994</creationdate><topic>asymptotic efficiency</topic><topic>blumen's test</topic><topic>Covariance matrices</topic><topic>Exact sciences and technology</topic><topic>Hyperplanes</topic><topic>location</topic><topic>Mathematical functions</topic><topic>Mathematical vectors</topic><topic>Mathematics</topic><topic>Nonparametric inference</topic><topic>Null hypothesis</topic><topic>Objective functions</topic><topic>oja median</topic><topic>one‐sample problem</topic><topic>P values</topic><topic>permutation test</topic><topic>Probability and statistics</topic><topic>randles's test</topic><topic>Random sampling</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>T distribution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hettmansperger, Thomas P.</creatorcontrib><creatorcontrib>Nyblom, Jukka</creatorcontrib><creatorcontrib>Oja, Hannu</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Periodicals Index Online Segment 18</collection><collection>Periodicals Index Online Segment 32</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access & Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access & Build (Plan A) - APAC</collection><collection>Primary Sources Access & Build (Plan A) - Canada</collection><collection>Primary Sources Access & Build (Plan A) - West</collection><collection>Primary Sources Access & Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - Midwest</collection><collection>Primary Sources Access & Build (Plan A) - North Central</collection><collection>Primary Sources Access & Build (Plan A) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</collection><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hettmansperger, Thomas P.</au><au>Nyblom, Jukka</au><au>Oja, Hannu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Affine Invariant Multivariate One-Sample Sign Tests</atitle><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle><date>1994-01-01</date><risdate>1994</risdate><volume>56</volume><issue>1</issue><spage>221</spage><epage>234</epage><pages>221-234</pages><issn>0035-9246</issn><issn>1369-7412</issn><eissn>2517-6161</eissn><eissn>1467-9868</eissn><coden>JSTBAJ</coden><abstract>Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies of the proposed test and the Oja multivariate median are given. Lower bounds for the efficiencies of the new test (and the Randles test) relative to the classical Hotelling test are established for elliptic alternatives and for unimodal elliptic alternatives. Relative efficiencies under multivariate t-distributions are also tabulated. The theory is illustrated by a simple example.</abstract><cop>London</cop><pub>Blackwell Publishers</pub><doi>10.1111/j.2517-6161.1994.tb01973.x</doi><tpages>14</tpages></addata></record> |
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| ispartof | Journal of the Royal Statistical Society. Series B, Methodological, 1994-01, Vol.56 (1), p.221-234 |
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| language | eng |
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| source | Periodicals Index Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | asymptotic efficiency blumen's test Covariance matrices Exact sciences and technology Hyperplanes location Mathematical functions Mathematical vectors Mathematics Nonparametric inference Null hypothesis Objective functions oja median one‐sample problem P values permutation test Probability and statistics randles's test Random sampling Sciences and techniques of general use Statistics T distribution |
| title | Affine Invariant Multivariate One-Sample Sign Tests |
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