IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i2d10.1007_s11749-021-00788-6.html
   My bibliography  Save this article

Tests for circular symmetry of complex-valued random vectors

Author

Listed:
  • Norbert Henze

    (Karlsruhe Institute of Technology (KIT))

  • Pierre Lafaye De Micheaux

    (UNSW Sydney
    Univ Montpellier, INSERM
    Université Paul-Valéry Montpellier 3)

  • Simos G. Meintanis

    (National and Kapodistrian University of Athens
    North-West University)

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 $$L^2$$ 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.

Suggested Citation

  • Norbert Henze & Pierre Lafaye De Micheaux & Simos G. Meintanis, 2022. "Tests for circular symmetry of complex-valued random vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 488-518, June.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:2:d:10.1007_s11749-021-00788-6
    DOI: 10.1007/s11749-021-00788-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-021-00788-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-021-00788-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    2. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    3. Henze, N. & Klar, B. & Meintanis, S. G., 2003. "Invariant tests for symmetry about an unspecified point based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 275-297, November.
    4. Andersson, Steen A. & Perlman, Michael D., 1984. "Two testing problems relating the real and complex multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 21-51, August.
    5. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    6. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    7. Gilles Ducharme & Pierre Lafaye de Micheaux & Bastien Marchina, 2016. "The complex multinormal distribution, quadratic forms in complex random vectors and an omnibus goodness-of-fit test for the complex normal distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 77-104, February.
    8. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    9. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    10. Bruce G. Lindsay & Marianthi Markatou & Surajit Ray, 2014. "Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 395-410, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    2. Sangyeol Lee & Simos G. Meintanis & Minyoung Jo, 2019. "Inferential procedures based on the integrated empirical characteristic function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 357-386, September.
    3. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    4. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.
    5. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    6. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    7. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    8. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    9. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    10. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    11. Norbert Henze & Celeste Mayer, 2020. "More good news on the HKM test for multivariate reflected symmetry about an unknown centre," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 741-770, June.
    12. Delgado, Miguel A. & Song, Xiaojun, 2018. "Nonparametric tests for conditional symmetry," Journal of Econometrics, Elsevier, vol. 206(2), pages 447-471.
    13. Tarik Bahraoui & Jean‐François Quessy, 2022. "Tests of multivariate copula exchangeability based on Lévy measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1215-1243, September.
    14. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    15. James S. Allison & Charl Pretorius, 2017. "A Monte Carlo evaluation of the performance of two new tests for symmetry," Computational Statistics, Springer, vol. 32(4), pages 1323-1338, December.
    16. Mirosław Krzyśko & Łukasz Smaga, 2020. "Measuring and Testing Mutual Dependence of Multivariate Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 21-37, September.
    17. Baringhaus, Ludwig & Gaigall, Daniel, 2023. "A goodness-of-fit test for the compound Poisson exponential model," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    18. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.
    19. Dai, Xinjie & Niu, Cuizhen & Guo, Xu, 2018. "Testing for central symmetry and inference of the unknown center," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 15-31.
    20. Norbert Henze & María Dolores Jiménez‐Gamero, 2021. "A test for Gaussianity in Hilbert spaces via the empirical characteristic functional," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 406-428, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:31:y:2022:i:2:d:10.1007_s11749-021-00788-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.