Nonparametric test for the homogeneity of the overall variability

作者：SenGupta Ashis; Hon Keung Tony Ng^*

来源：Journal of Applied Statistics, 2011, 38(9): 1751-1768.

DOI：10.1080/02664763.2010.529876

• generalized variance
• multivariate distribution
• bivariate Cauchy
• bivariate Pareto
• permutation method
• Monte Carlo method

In this paper, we propose a nonparametric test for homogeneity of overall variabilities for two multidimensional populations. Comparisons between the proposed nonparametric procedure and the asymptotic parametric procedure and a permutation test based on standardized generalized variances are made when the underlying populations are multivariate normal. We also study the performance of these test procedures when the underlying populations are non-normal. We observe that the nonparametric procedure and the permutation test based on standardized generalized variances are not as powerful as the asymptotic parametric test under normality. However, they are reliable and powerful tests for comparing overall variability under other multivariate distributions such as the multivariate Cauchy, the multivariate Pareto and the multivariate exponential distributions, even with small sample sizes. A Monte Carlo simulation study is used to evaluate the performance of the proposed procedures. An example from an educational study is used to illustrate the proposed nonparametric test.

• 出版日期2011