On a Class of Multivariate Multisample Rank Order Tests II

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Excerpt from On a Class of Multivariate Multisample Rank Order Tests II: Tests for Homogeneity of Dispersion MatricesIn the parametric theory, the problem of testing homogeneity of dispersion matrices has nothing to do with the homogeneity of location parameters. However, in the nonparametric case the formulation of the hypothesis of invariance deems the identity of distributions, and this, in turn requires the homogeneity of location parameters. Thus we consider the following problems: (i) Tests for the homogeneity of dispersion matrices assuming the identity of location parameters. Some permutationally distribution free tests for this problem are considered here and their large sample properties are studied, (ii) Tests for the homogeneity of dispersion matrices without assuming the identity of location parameters. Here the basic permutation argument is not tenable, and only large sample properties are considered. Finally (iii) the problem of testing simultaneously the homogeneity of location parameters as well as the dispersion matrices is briefly discussed.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.