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A class of percentile modified Lepage-type tests

Author

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  • Amitava Mukherjee

    (XLRI-Xavier School of Management)

  • Marco Marozzi

    (University of Venice)

Abstract

The two-sample problem usually tests for a difference in location. However, there are many situations, for example in biomedicine, where jointly testing for difference in location and variability may be more appropriate. Moreover, heavy-tailed data, outliers and small-sample sizes are common in biomedicine and in other fields. These considerations make the use of nonparametric methods more appealing than parametric ones. The aim of the paper is to contribute to the literature about nonparametric simultaneous location and scale testing. More precisely, several existing tests are generalized and unified, and a new class of tests based on the Mahalanobis distance between the percentile modified test statistics for location and scale differences is introduced. The asymptotic distributions of the test statistics are obtained, and small-sample size behaviour of the tests is studied and compared to other tests via Monte Carlo simulations. It is shown that the proposed class of tests performs well when there are differences in both location and variability. A practical application is presented.

Suggested Citation

  • Amitava Mukherjee & Marco Marozzi, 2019. "A class of percentile modified Lepage-type tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 657-689, August.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:6:d:10.1007_s00184-018-0700-1
    DOI: 10.1007/s00184-018-0700-1
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    References listed on IDEAS

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    1. Cuizhen Niu & Xu Guo & Wangli Xu & Lixing Zhu, 2014. "Testing equality of shape parameters in several inverse Gaussian populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 795-809, August.
    2. Marco Marozzi, 2014. "The multisample Cucconi test," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 209-227, June.
    3. Murakami, Hidetoshi, 2007. "Lepage type statistic based on the modified Baumgartner statistic," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5061-5067, June.
    4. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    5. Markus Pauly, 2011. "Discussion about the quality of F-ratio resampling tests for comparing variances," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 163-179, May.
    6. Marozzi, Marco, 2004. "A bi-aspect nonparametric test for the two-sample location problem," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 639-648, January.
    7. Erich Lehmann, 2009. "Parametric versus nonparametrics: two alternative methodologies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 397-405.
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    Cited by:

    1. Yamaguchi, Hikaru & Murakami, Hidetoshi, 2023. "The multi-aspect tests in the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).

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