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.
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Acknowledgements
Research on this topic was initiated during the third author’s visit to the UNSW. Simos Meintanis would like to sincerely thank Pierre Lafaye de Micheaux and the School of Mathematics and Statistics of the UNSW for making this visit possible. This research includes computations using the computational cluster Katana supported by Research Technology Services at UNSW Sydney. The authors would like to thank two anonymous referees for many valuable remarks.
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Henze, N., Lafaye De Micheaux, P. & Meintanis, S.G. Tests for circular symmetry of complex-valued random vectors. TEST 31, 488–518 (2022). https://doi.org/10.1007/s11749-021-00788-6
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DOI: https://doi.org/10.1007/s11749-021-00788-6