## Graphical and formal statistical tools for the symmetry of bivariate copulas.(English. French summary)Zbl 1351.62117

Summary: Statistical tools to check whether the underlying copula of a pair of random variables is symmetric are developed. The proposed methods are based on the theoretical and empirical versions of the C-power functions introduced and formally studied by the authors [J. Multivariate Anal. 129, 16–36 (2014; Zbl 1288.62095)]. On one part, a methodology is developed for testing the null hypothesis that the copula of a given population is symmetric. To this end, a sequential testing procedure is proposed where at each level, the $$P$$-value is estimated with the help of the multiplier bootstrap method. On another side, a related graphical method is proposed in order to gain an idea of the degree of asymmetry in bivariate data. The good properties of the methods in small samples are investigated with the help of Monte Carlo simulations under various scenarios of symmetric and asymmetric dependence. The newly introduced procedures are used to analyse the Nutrient and the Walker Lake data sets.

### MSC:

 62H15 Hypothesis testing in multivariate analysis 62H20 Measures of association (correlation, canonical correlation, etc.) 62P10 Applications of statistics to biology and medical sciences; meta analysis

Zbl 1288.62095

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### References:

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