On the Theory of Rank Order Tests for Location in the Multivariate One Sample Problem

Abstract

In the multivariate one sample location problem, the theory of permutation distribution under sign-invariant transformations is extended to a class of rank order statistics, and this is utilized in the formulation of a genuinely distribution free class of rank order tests for location (based on Chernoff-Savage (1958) type of test-statistics). Asymptotic properties of these permutationally distribution free rank order tests are studied, and certain stochastic equivalence relations with a similar class of multivariate extensions of one sample Chernoff-Savage type of tests are derived. The power properties of these tests are studied.