On the Estimation of Location Parameters in the Multivariate One-Sample and Two-Sample Problems (Classic Reprint)

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Excerpt from On the Estimation of Location Parameters in the Multivariate One-Sample and Two-Sample Problems Estimates of location parameters based on rank order tests in the univariate one-sample and two-sample problems have been considered by various authors. For the details of references, the reader is referred to the most recent papers of Gastwirth [4] and Bloch and Gastwirth In this paper we consider the estimates of location parameters in the multivariate one-sample and two-sample problems. These estimates are obtained through the use of coordinate wise rank order test statistics such as the Wilcoxon or normal scores statistic considered by the authors in [9] and The distribution of these estimates is shown to be symmetric with respect to the parameters being estimated. These estimates are also translation-invariant and robust. Furthermore the estimates are shown to be asymptotically normal. Finally the asymptotic efficiencies of these estimates relative to the estimates based on the vectors of means and medians are obtained by applying the criterion of Wilks generalized variance. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.