A Note on Test of Homogeneity Against Umbrella Scale Alternative Based on U-Statistics

Abstract: A fundamental problem encountered in statistics is that of testing the equality of scale parameters against umbrella alternative with at least one strict inequality. In this article, a nonparametric test based on U-statistic by considering the subsample minima and maxima for several sample scale problem against umbrella alternative, when peak of the umbrella is known, is proposed. The proposed test have the advantage of not requiring the several distribution functions to have a common median, but rather any common quantile of order 1 0 ,   q q , (not necessarily 1⁄2) which is assumed to be known. Pitman efficiency indicate that the proposed test is equivalent to the test B proposed by Gaur, Mahajan and Arora (2012).