On the exact region determined by Spearman’s ρ and Blest’s measure of rank correlation ν for bivariate extreme-value copulas

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis Pub Date : 2024-10-09 DOI:10.1016/j.jmva.2024.105377

Marco Tschimpke

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引用次数: 0

Abstract

Considering pairs of measures of association it has been of interest how much the values of one measure varies, fixing the value of the other one. Motivated by this fact, we establish sharp lower and upper bounds for the region determined by Spearman’s

ρ

and Blest’s measure of rank correlation

ν

for bivariate extreme-value copulas (EVCs). Moreover, in the well-studied class of EVCs, exact regions for Spearman’s footrule

ϕ

/Blomqvist’s

β

and Spearman’s

ρ

, Kendall’s

τ

or Blest’s symmetrised measure of rank correlation

ξ

are provided. A performance analysis comparing rank-based estimators of

ρ

and

ν

with estimators using that the sample is drawn from an extreme-value copula concludes this paper.

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关于斯皮尔曼ρ和布莱斯特等级相关性ν对二元极值共存关系的测量所确定的确切区域

考虑到成对的相关性度量，一个度量的值在固定另一个度量的值的情况下会有多大的变化一直是人们感兴趣的问题。受这一事实的启发，我们为二元极值协方差（EVCs）的斯皮尔曼ρ和布莱斯特等级相关度ν所决定的区域建立了尖锐的下限和上限。此外，在研究充分的 EVCs 类别中，还提供了斯皮尔曼脚规 ϕ/Blomqvist β 和斯皮尔曼 ρ、肯德尔 τ 或 Blest 对称等级相关性度量 ξ 的精确区域。本文最后对基于秩的 ρ 和 ν 估计器与使用极值协程抽取样本的估计器进行了性能分析比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Multivariate Analysis 数学-统计学与概率论

CiteScore

2.40

自引率

25.00%

发文量

108

审稿时长

74 days

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.