On the Asymptotic Distribution of a General Measure of Monotone Dependence
In this paper the asymptotic normality of a class of statistics, including Gini's index of cograduation and Spearman's rank correlation coefficient, is proved. The asymptotic normality is stated under a large class of alternatives including the bivariate distributions corresponding to a co...
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| Veröffentlicht in: | The Annals of statistics 1996-06, Vol.24 (3), p.1386-1399 |
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| container_end_page | 1399 |
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| container_issue | 3 |
| container_start_page | 1386 |
| container_title | The Annals of statistics |
| container_volume | 24 |
| creator | Cifarelli, Donato Michele Conti, Pier Luigi Regazzini, Eugenio |
| description | In this paper the asymptotic normality of a class of statistics, including Gini's index of cograduation and Spearman's rank correlation coefficient, is proved. The asymptotic normality is stated under a large class of alternatives including the bivariate distributions corresponding to a condition of lack of association introduced in Section 3. The problems of testing the hypothesis of lack of association and of constructing confidence intervals for the population index of cograduation are also considered. |
| doi_str_mv | 10.1214/aos/1032526975 |
| format | Article |
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The problems of testing the hypothesis of lack of association and of constructing confidence intervals for the population index of cograduation are also considered.</description><identifier>ISSN: 0090-5364</identifier><identifier>EISSN: 2168-8966</identifier><identifier>DOI: 10.1214/aos/1032526975</identifier><identifier>CODEN: ASTSC7</identifier><language>eng</language><publisher>Hayward, CA: Institute of Mathematical Statistics</publisher><subject>62E20 ; 62G10 ; 62H20 ; Ambivalence ; Consistent estimators ; Correlation coefficients ; Correlations ; Distribution theory ; Empirical processes ; Exact sciences and technology ; functional limit theorem ; Gini index ; index of cograduation ; lack of association (= indifference) ; Mathematical inequalities ; Mathematics ; monotone dependence ; Multivariate analysis ; Nonparametric inference ; Nonparametrics ; Perceptron convergence procedure ; Probability and statistics ; Sciences and techniques of general use ; Statistical theories ; Statistical variance ; Statistics ; U-statistics</subject><ispartof>The Annals of statistics, 1996-06, Vol.24 (3), p.1386-1399</ispartof><rights>Copyright 1996 Institute of Mathematical Statistics</rights><rights>1996 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-ff1b3cd35c0a3ad99712af29ae57ed3c09b2e123ad4cab4f8db153f280c5ba523</citedby><cites>FETCH-LOGICAL-c384t-ff1b3cd35c0a3ad99712af29ae57ed3c09b2e123ad4cab4f8db153f280c5ba523</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2242600$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2242600$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,803,832,885,926,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3236922$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Cifarelli, Donato Michele</creatorcontrib><creatorcontrib>Conti, Pier Luigi</creatorcontrib><creatorcontrib>Regazzini, Eugenio</creatorcontrib><title>On the Asymptotic Distribution of a General Measure of Monotone Dependence</title><title>The Annals of statistics</title><description>In this paper the asymptotic normality of a class of statistics, including Gini's index of cograduation and Spearman's rank correlation coefficient, is proved. 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The problems of testing the hypothesis of lack of association and of constructing confidence intervals for the population index of cograduation are also considered.</description><subject>62E20</subject><subject>62G10</subject><subject>62H20</subject><subject>Ambivalence</subject><subject>Consistent estimators</subject><subject>Correlation coefficients</subject><subject>Correlations</subject><subject>Distribution theory</subject><subject>Empirical processes</subject><subject>Exact sciences and technology</subject><subject>functional limit theorem</subject><subject>Gini index</subject><subject>index of cograduation</subject><subject>lack of association (= indifference)</subject><subject>Mathematical inequalities</subject><subject>Mathematics</subject><subject>monotone dependence</subject><subject>Multivariate analysis</subject><subject>Nonparametric inference</subject><subject>Nonparametrics</subject><subject>Perceptron convergence procedure</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Statistical theories</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>U-statistics</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNplUD1vwjAUtKpWKqVdO3XI0DXgjzjEWxH0UyCWMkcvzrNqFGxkm4F_XxARHTqddPfu3ukIeWR0xDgrxuDjmFHBJS_VRF6RAWdllVeqLK_JgFJFcynK4pbcxbihlEpViAH5Wrks_WA2jYftLvlkdTa3MQXb7JP1LvMmg-wdHQbosiVC3Ac8kUvvfPIOsznu0LXoNN6TGwNdxIceh2T99vo9-8gXq_fP2XSRa1EVKTeGNUK3QmoKAlqlJoyD4QpQTrAVmqqGI-NHqdDQFKZqGyaF4RXVsgHJxZC8nHN3wW9QJ9zrzrb1LtgthEPtwdaz9aJnezhuU_9tc4wYnSN08DEGNBc3o_VpzP-G5_4nRA2dCeC0jReX4KJU_FTt6Xy2icmHi8x5wUtKxS9ZIH92</recordid><startdate>19960601</startdate><enddate>19960601</enddate><creator>Cifarelli, Donato Michele</creator><creator>Conti, Pier Luigi</creator><creator>Regazzini, Eugenio</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>19960601</creationdate><title>On the Asymptotic Distribution of a General Measure of Monotone Dependence</title><author>Cifarelli, Donato Michele ; Conti, Pier Luigi ; Regazzini, Eugenio</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-ff1b3cd35c0a3ad99712af29ae57ed3c09b2e123ad4cab4f8db153f280c5ba523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>62E20</topic><topic>62G10</topic><topic>62H20</topic><topic>Ambivalence</topic><topic>Consistent estimators</topic><topic>Correlation coefficients</topic><topic>Correlations</topic><topic>Distribution theory</topic><topic>Empirical processes</topic><topic>Exact sciences and technology</topic><topic>functional limit theorem</topic><topic>Gini index</topic><topic>index of cograduation</topic><topic>lack of association (= indifference)</topic><topic>Mathematical inequalities</topic><topic>Mathematics</topic><topic>monotone dependence</topic><topic>Multivariate analysis</topic><topic>Nonparametric inference</topic><topic>Nonparametrics</topic><topic>Perceptron convergence procedure</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistical theories</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>U-statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cifarelli, Donato Michele</creatorcontrib><creatorcontrib>Conti, Pier Luigi</creatorcontrib><creatorcontrib>Regazzini, Eugenio</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>Cifarelli, Donato Michele</au><au>Conti, Pier Luigi</au><au>Regazzini, Eugenio</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Asymptotic Distribution of a General Measure of Monotone Dependence</atitle><jtitle>The Annals of statistics</jtitle><date>1996-06-01</date><risdate>1996</risdate><volume>24</volume><issue>3</issue><spage>1386</spage><epage>1399</epage><pages>1386-1399</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>In this paper the asymptotic normality of a class of statistics, including Gini's index of cograduation and Spearman's rank correlation coefficient, is proved. 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| ispartof | The Annals of statistics, 1996-06, Vol.24 (3), p.1386-1399 |
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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 | 62E20 62G10 62H20 Ambivalence Consistent estimators Correlation coefficients Correlations Distribution theory Empirical processes Exact sciences and technology functional limit theorem Gini index index of cograduation lack of association (= indifference) Mathematical inequalities Mathematics monotone dependence Multivariate analysis Nonparametric inference Nonparametrics Perceptron convergence procedure Probability and statistics Sciences and techniques of general use Statistical theories Statistical variance Statistics U-statistics |
| title | On the Asymptotic Distribution of a General Measure of Monotone Dependence |
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