Testing Conditional Tail Independence

Measuring tail dependence structure is crucial in understanding the behavior 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.