A class of nonparametric tests for testing homogeneity of variances against ordered alternatives based on subsample extrema

A class of nonparametric test statistics for several sample scale problem is proposed by considering extrema of subsamples of size c. The proposed class of statistics has the advantage of not requiring the several distribution functions to have a common median, but rather any common quantité of order α, 0 ≤ α ≤ 1, (not necessarily 1/ 2) which is assumed to be known. The proposed class of tests is compared with other known tests already existing in the literature in the Pitman asymptotic relative efficiency sense for different distributions. Some results of Monte Carlo power study are also presented.