We propose tests for the null hypothesis that the law of a complex-valued random vector is circularly symmetric. The test criteria are formulated as $L^2$-type criteria based on empirical characteristic functions, and they are convenient from the computational point of view. Asymptotic as well as Monte-Carlo results are presented. Applications on real data are also reported. An R package called CircSymTest is available from the authors.

翻译：我们建议对复合价值随机矢量法是循环对称的无效假设进行测试。测试标准是根据经验特性功能拟订的2美元标准类型,从计算角度来说是方便的。介绍了Asymptatic和Monte-Carlo的结果。还报告了对真实数据的应用。作者提供了称为CircSymTest的R软件包。