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Abstract:
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The problem of detecting monotonic increasing/decreasing trends in variances from k samples is widely met in many applications, e.g. financial data analysis, medical and environmental studies. However, most of the tests for homogeneity of variances against ordered alternatives rely on the assumption of normality. They are often non-robust with respect to its violation, which eventually leads to unreliable conclusions. In this talk, we propose a combination of a robust Levene-type test and a finite-intersection method, which relaxes the assumption of normality. The new combined procedure yields a more accurate estimate of sizes of the test and provides competitive powers. In addition, we discuss various modifications of the proposed test for unbalanced design cases. We present theoretical justifications of the new test and illustrate its application by simulations and case studies.
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