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A unified approach to goodness-of-fit testing for spherical and hyperspherical data

Author

Listed:
  • Bruno Ebner

    (Karlsruhe Institute of Technology (KIT))

  • Norbert Henze

    (Karlsruhe Institute of Technology (KIT))

  • Simos Meintanis

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

Abstract

We propose a general and relatively simple method to construct goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function, and it leads to test criteria that are convenient regarding applications and consistent against arbitrary deviations from the model under test. We emphasize goodness-of-fit tests for spherical distributions due to their importance in applications and the relative scarcity of available methods.

Suggested Citation

  • Bruno Ebner & Norbert Henze & Simos Meintanis, 2024. "A unified approach to goodness-of-fit testing for spherical and hyperspherical data," Statistical Papers, Springer, vol. 65(6), pages 3447-3475, August.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-024-01529-1
    DOI: 10.1007/s00362-024-01529-1
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    References listed on IDEAS

    as
    1. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    2. L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.
    3. 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.
    4. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    5. Hao Chen & Yin Xia, 2023. "A Normality Test for High-dimensional Data Based on the Nearest Neighbor Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 719-731, January.
    6. 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.
    7. Ebner, Bruno & Henze, Norbert & Yukich, Joseph E., 2018. "Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 231-242.
    8. Bruno Ebner & Norbert Henze, 2020. "Rejoinder on: 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 911-913, December.
    9. J. L. Scealy & Andrew T. A. Wood, 2019. "Scaled von Mises–Fisher Distributions and Regression Models for Paleomagnetic Directional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1547-1560, October.
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