Combinazione non parametrica di statistiche basate sulle mediane per il problema di Behrens-Fisher multivariato

Abstract

James (1954), Ying Yao (1965), Ballin-Pesarin (1990) have proposed approximate solutions of the Behrens-Fisher p-variate problem. The last-mentioned is regarded as the best in approximating both the nominal significance level and the power. This solution is based on the nonparametric combination of p permutation tests, each referring to p marginal hypotheses. In Ballin-Pesarin solution, the marginal tests used are Welch's statistical tests, which, as is well known, do not strictly respect the principle of permutation inasmuch as they are quasi-invariant with respect to unknown variance ratios. In this paper, I propose a marginal permutation test of sample medians. I believe that, in order to comply more fully with the invariant properties of permutational distribution of the median as opposed to the mean, such medians improve the approximation of the nominal significance level and the exact power. It is proved, moreover, that the proposed marginal test is unbiased and consistent.