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In this paper, we develop copula-based measures and testing procedures for the conditional asymmetry of a random variable given another. The resulting tests are ranked based and thus robust to the outliers. The asymptotic properties of the test statistics are investigated. Simulation studies and real data analysis are conducted to illustrate the performance of the proposed tests. [ABSTRACT FROM AUTHOR]

The assumption of conditional symmetry, which implies that the distribution of one random variable given another random variable has a symmetric form, plays a crucial role in various probability and statistics problems. This study aims to examine copula properties related to the conditional symmetry/asymmetry of two random variables. We investigate the possibility of ordering copulas based on their level of conditional asymmetry, similar to the concordance ordering for dependence. To quantify the degree of conditional asymmetry of a copula, we introduce measures that are monotonic for the proposed ordering. The characteristics of the proposed order and measures are elaborated upon. Several examples are included to demonstrate the results. [ABSTRACT FROM AUTHOR]