Tests for circular symmetry of complex-valued random vectors

Norbert Henze (1) , Pierre Lafaye de Micheaux (2, 3, 4) , Simos Meintanis (5, 6)

1 KIT - Karlsruhe Institute of Technology
2 UNSW Faculty of Medicine [Sydney]
3 IDESP - Institut Desbrest de santé publique
4 UPVM - Université Paul-Valéry - Montpellier 3
5 NKUA - National and Kapodistrian University of Athens
6 NWU - North-West University [Potchefstroom]

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 L2-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.

Mots clés: Complex-valued random variable; Characteristic function; Goodness-of -fit test

Domaines: Statistiques [math.ST]

Norbert Henze, Pierre Lafaye de Micheaux, Simos Meintanis. Tests for circular symmetry of complex-valued random vectors. Test, 2021, 31, pp.488-518. ⟨10.1007/s11749-021-00788-6⟩. ⟨hal-03675738⟩