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Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives

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  • Kimihiro Noguchi
  • Yulia Gel

Abstract

The problem of detecting monotonic trends in variances from k samples is widely met in many applications, e.g. finance, economics, medicine, biopharmaceutical, and environmental studies. However, most of the tests for equality of variances against ordered alternatives rely on the assumption of normality and are often non-robust to its violation, which eventually leads to unreliable conclusions. In this paper, we propose a new distribution-free test against trends in variances which is based on a combination of a robust Levene-type approach and a finite-intersection method. The new test can be viewed as a piecewise linear approximation to possibly non-linear dynamics of variances, and hence is applicable to a broad range of alternatives. The new combined procedure yields a more accurate estimate of size and provides a competitive power for a variety of distributions and alternatives. In addition, we develop a modification of the proposed test for unbalanced designs with small sample sizes. We discuss asymptotic properties of the new test and illustrate its applications with simulations and case studies from soil pollution analysis, real estate markets, engineering, and epidemiology.

Suggested Citation

  • Kimihiro Noguchi & Yulia Gel, 2010. "Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 897-913.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:897-913
    DOI: 10.1080/10485251003698505
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    Cited by:

    1. Ryan C. Erps & Kimihiro Noguchi, 2020. "A Robust Test for Checking the Homogeneity of Variability Measures and Its Application to the Analysis of Implicit Attitudes," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 403-425, August.
    2. I. Parra-Frutos, 2013. "Testing homogeneity of variances with unequal sample sizes," Computational Statistics, Springer, vol. 28(3), pages 1269-1297, June.
    3. I. Parra-Frutos, 2016. "Preliminary tests when comparing means," Computational Statistics, Springer, vol. 31(4), pages 1607-1631, December.
    4. Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.

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