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

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.