{"title":"多变量定向尾加权依赖性测量法","authors":"Xiaoting Li, Harry Joe","doi":"10.1016/j.jmva.2024.105319","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a new family of directional dependence measures for multivariate distributions. The family of dependence measures is indexed by <span><math><mrow><mi>α</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. When <span><math><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></math></span>, they measure the strength of dependence along different paths to the joint upper or lower orthant. For <span><math><mi>α</mi></math></span> large, they become tail-weighted dependence measures that put more weight in the joint upper or lower tails of the distribution. As <span><math><mrow><mi>α</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, we show the convergence of the directional dependence measures to the multivariate tail dependence function and characterize the convergence pattern with an asymptotic expansion. This expansion leads to a method to estimate the multivariate tail dependence function using weighted least square regression. We develop rank-based sample estimators for the tail-weighted dependence measures and establish their asymptotic distributions. The practical utility of the tail-weighted dependence measures in multivariate tail inference is further demonstrated through their application to a financial dataset.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000265/pdfft?md5=b41054186655fc814404cc641ffc0dfe&pid=1-s2.0-S0047259X24000265-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Multivariate directional tail-weighted dependence measures\",\"authors\":\"Xiaoting Li, Harry Joe\",\"doi\":\"10.1016/j.jmva.2024.105319\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose a new family of directional dependence measures for multivariate distributions. The family of dependence measures is indexed by <span><math><mrow><mi>α</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. When <span><math><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></math></span>, they measure the strength of dependence along different paths to the joint upper or lower orthant. For <span><math><mi>α</mi></math></span> large, they become tail-weighted dependence measures that put more weight in the joint upper or lower tails of the distribution. As <span><math><mrow><mi>α</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, we show the convergence of the directional dependence measures to the multivariate tail dependence function and characterize the convergence pattern with an asymptotic expansion. This expansion leads to a method to estimate the multivariate tail dependence function using weighted least square regression. We develop rank-based sample estimators for the tail-weighted dependence measures and establish their asymptotic distributions. The practical utility of the tail-weighted dependence measures in multivariate tail inference is further demonstrated through their application to a financial dataset.</p></div>\",\"PeriodicalId\":16431,\"journal\":{\"name\":\"Journal of Multivariate Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0047259X24000265/pdfft?md5=b41054186655fc814404cc641ffc0dfe&pid=1-s2.0-S0047259X24000265-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Multivariate Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0047259X24000265\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X24000265","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
We propose a new family of directional dependence measures for multivariate distributions. The family of dependence measures is indexed by . When , they measure the strength of dependence along different paths to the joint upper or lower orthant. For large, they become tail-weighted dependence measures that put more weight in the joint upper or lower tails of the distribution. As , we show the convergence of the directional dependence measures to the multivariate tail dependence function and characterize the convergence pattern with an asymptotic expansion. This expansion leads to a method to estimate the multivariate tail dependence function using weighted least square regression. We develop rank-based sample estimators for the tail-weighted dependence measures and establish their asymptotic distributions. The practical utility of the tail-weighted dependence measures in multivariate tail inference is further demonstrated through their application to a financial dataset.
期刊介绍:
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.