Tests for circular symmetry of complex-valued random vectors

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.