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Multivariate tests of uniformity

Author

Listed:
  • Mengta Yang

    (George Washington University)

  • Reza Modarres

    (George Washington University)

Abstract

We present tests of multivariate uniformity using data depth, the normal quantiles and the interpoint distances between the observations. We investigate the properties of the interpoint distances among uniform random vectors. We compare the performance of the proposed tests with two existing statistics under the hypothesis of uniformity and obtain their empirical power under various alternatives in a Monte Carlo study.

Suggested Citation

  • Mengta Yang & Reza Modarres, 2017. "Multivariate tests of uniformity," Statistical Papers, Springer, vol. 58(3), pages 627-639, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0715-x
    DOI: 10.1007/s00362-015-0715-x
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    References listed on IDEAS

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    1. M. Pardo, 2003. "A test for uniformity based on informational energy," Statistical Papers, Springer, vol. 44(4), pages 521-534, October.
    2. Karl Mosler, 2003. "Central Regions and Dependency," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 5-21, March.
    3. Pavlo Mozharovskyi & Karl Mosler & Tatjana Lange, 2015. "Classifying real-world data with the $${ DD}\alpha $$ D D α -procedure," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(3), pages 287-314, September.
    4. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    5. Y. A. S. Hegazy & J. R. Green, 1975. "Some New Goodness‐Of‐Fit Tests Using Order Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(3), pages 299-308, November.
    6. Zhenyu Liu & Reza Modarres, 2011. "Lens data depth and median," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1063-1074.
    7. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    8. Petrie, Adam & Willemain, Thomas R., 2013. "An empirical study of tests for uniformity in multidimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 253-268.
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    Cited by:

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