{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"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\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"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\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0047259X24000265\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X24000265","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.