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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

Author

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  • Jiajuan Liang

    (University of New Haven)

  • Kai Wang Ng

    (The University of Hong Kong)

  • Guoliang Tian

    (Southern University of Science and Technology)

Abstract

In this paper we employ the conditional probability integral transformation (CPIT) method to transform a d-dimensional sample from two classes of generalized multivariate distributions into a uniform sample in the unit interval $$(0,\,1)$$ ( 0 , 1 ) or in the unit hypercube $$[0,\,1]^{d-1}$$ [ 0 , 1 ] d - 1 ( $$d\ge 2$$ d ≥ 2 ). A class of existing uniform statistics are adopted to test the uniformity of the transformed sample. Monte Carlo studies are carried out to demonstrate the performance of the tests in controlling type I error rates and power against a selected group of alternative distributions. It is concluded that the proposed tests have satisfactory empirical performance and the CPIT method in this paper can serve as a general way to construct goodness-of-fit tests for many generalized multivariate distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0630-0
    DOI: 10.1007/s10463-017-0630-0
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    References listed on IDEAS

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    1. Huffer, Fred W. & Park, Cheolyong, 2007. "A test for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 256-281, February.
    2. Schott, James R., 2002. "Testing for elliptical symmetry in covariance-matrix-based analyses," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 395-404, December.
    3. Zhu, Li-Xing & Neuhaus, Georg, 2003. "Conditional tests for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 284-298, February.
    4. Jiajuan Liang & Kai-Tai Fang & Fred Hickernell, 2008. "Some necessary uniform tests for spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 679-696, September.
    5. Jiajuan Liang & Kai Ng, 2008. "A method for generating uniformly scattered points on the L p -norm unit sphere and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 83-98, June.
    6. Manzotti, A. & Pérez, Francisco J. & Quiroz, Adolfo J., 2002. "A Statistic for Testing the Null Hypothesis of Elliptical Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 274-285, May.
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    Cited by:

    1. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.

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