Tests for circular symmetry of complex-valued random vectors

TL;DR

This paper introduces computationally efficient tests for assessing the circular symmetry of complex-valued random vectors using empirical characteristic functions, supported by theoretical and simulation results, with practical applications and an R package.

Contribution

It presents new $L^2$-type tests for circular symmetry based on empirical characteristic functions, with asymptotic and Monte Carlo validation, and provides an R package for implementation.

Findings

Tests effectively detect circular symmetry violations.

The methods are computationally convenient.

Applications demonstrate practical utility.

Abstract

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.