Abstract

Measuring tail dependence structure is crucial in understanding the be

havior of bivariate extremes. Common measures of tail dependence include tail

dependence index, coefficient of tail dependence, tail dependence function, and

so on. However, in practice, there may exist covariates which are related with

both variables. Up to our knowledge, there is no measure that focuses on the

conditional tail dependence structure. This paper first introduces the concept of

conditional tail dependence index, based on which we can distinguish between

conditional tail independence and conditional tail dependence. We provide a test

statistic named conditional tail quotient correlation coefficient (CTQCC) to test

the null hypothesis of conditional tail independence and obtain its asymptotic

distribution. Simulation studies are conducted to assess the finite sample performance of the proposed method. We apply CTQCC to investigate conditional

tail dependencies of a large-scale problem of daily precipitation and daily average

wind speed in the United States, given the daily maximum temperature. The

results show that the proposed method is effective in detecting conditional tail

dependence structures.

Information

Preprint No.SS-2025-0139
Manuscript IDSS-2025-0139
Complete AuthorsZhaowen Wang, Huixia Judy Wang, Deyuan Li
Corresponding AuthorsDeyuan Li
Emailsdeyuanli@fudan.edu.cn

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Acknowledgments

The authors thank the editor, associate editor, and reviewers for their

valuable comments and suggestions.

Deyuan Li’s research was partially

supported by the National Natural Science Foundation of China grant

12471279.

Supplementary Materials

The supplementary material contains the proofs of Proposition 1 and Theorem 1.

Supplementary materials are available for download.