Tests of symmetry for bivariate copulas. (English) Zbl 1440.62182
Summary: Tests are proposed for the hypothesis that the underlying copula of a continuous random pair is symmetric. The procedures are based on Cramér-von Mises and Kolmogorov-Smirnov functionals of a rank-based empirical process whose large-sample behaviour is obtained. The asymptotic validity of a re-sampling method to compute \(P\) values is also established. The technical arguments supporting the use of a Chi-squared test due to Jasson are also presented. A power study suggests that the proposed tests are more powerful than Jasson’s procedure under many scenarios of copula asymmetry. The methods are illustrated on a nutrient data set.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62G10 | Nonparametric hypothesis testing |
| 62G30 | Order statistics; empirical distribution functions |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
empirical copula process; exchangeability; multiplier central limit theorem; ranks; symmetryReferences:
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