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Statistica Sinica 27 (2017), 685-709

RANDOM THRESHOLD DRIVEN TAIL DEPENDENCE
MEASURES WITH APPLICATION TO
PRECIPITATION DATA ANALYSIS
Zhengjun Zhang, Chunming Zhang and Qiurong Cui
University of Wisconsin

Abstract: This paper first studies the theoretical properties of the tail quotient correlation coefficient (TQCC) which was proposed to measure tail dependence between two random variables. By introducing random thresholds in TQCC, an approximation theory between conditional tail probabilities is established. The new random threshold-driven TQCC can be used to test the null hypothesis of tail independence under which TQCC test statistics are shown to follow a Chi-squared distribution under two general scenarios. The TQCC is shown to be consistent under the alternative hypothesis of tail dependence with a general approximation of max-stable distribution. Second, we apply TQCC to investigate tail dependencies of a large scale problem of daily precipitation in the continental US. Our results, from the perspective of tail dependence, reveal nonstationarity, spatial clusters, and tail dependence from the precipitations across the continental US.

Key words and phrases: Climate extremes, conditional tail probability approximation, extreme value theory, hypothesis testing, nonlinear dependence.

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