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Conditional tests for elliptical symmetry

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  • Zhu, Li-Xing
  • Neuhaus, Georg

Abstract

In this paper, we suggest the conditional test procedures for testing elliptical symmetry of multivariate distribution. The conditional tests are exactly valid if the symmetric center and the shape matrix are given and are asymptotically valid if they are unknowns to be estimated. The equivalence, in the large sample sense, between the conditional tests and their unconditional counterparts is established. The power behavior of the tests under global as well as local alternatives is investigated theoretically. A small simulation study is performed.

Suggested Citation

  • Zhu, Li-Xing & Neuhaus, Georg, 2003. "Conditional tests for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 284-298, February.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:2:p:284-298
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    References listed on IDEAS

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    1. Baringhaus, L. & Henze, N., 1991. "Limit distributions for measures of multivariate skewness and kurtosis based on projections," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 51-69, July.
    2. Julian Besag & Peter J. Diggle, 1977. "Simple Monte Carlo Tests for Spatial Pattern," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 327-333, November.
    3. Fang, K. T. & Zhu, L. X. & Bentler, P. M., 1993. "A Necessary Test of Goodness of Fit for Sphericity," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 34-55, April.
    4. David Blough, 1989. "Multivariate symmetry via projection pursuit," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 461-475, September.
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    Cited by:

    1. Jiajuan Liang & Kai Wang Ng & Guoliang Tian, 2019. "A class of uniform tests for goodness-of-fit of the multivariate $$L_p$$ L p -norm spherical distributions and the $$l_p$$ l p -norm symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 137-162, February.
    2. Niu, Cuizhen & Guo, Xu & Li, Yong & Zhu, Lixing, 2018. "Pairwise distance-based tests for conditional symmetry," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 145-162.
    3. Stephanie Chan & Xuan Wang & Ina Jazić & Sarah Peskoe & Yingye Zheng & Tianxi Cai, 2021. "Developing and evaluating risk prediction models with panel current status data," Biometrics, The International Biometric Society, vol. 77(2), pages 599-609, June.
    4. Huffer, Fred W. & Park, Cheolyong, 2007. "A test for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 256-281, February.
    5. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    6. Boente, Graciela & Salibián Barrera, Matías & Tyler, David E., 2014. "A characterization of elliptical distributions and some optimality properties of principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 254-264.

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