MAJORIZATION METHODS ON HYPERPLANES AND THEIR APPLICATIONS

Let Z be a k(greater than or equal to 3) dimensional random vector with exchangeable components whose sum is zero, D a Schur-convex subset of the Euclidean k space R(k), and Omega the k - 1 dimensional hyperplane of R(k) consisting of all vector parameters whose components sum up to zero. Let psi(mu), mu is an element of Omega, denote the probability of Z + mu taking values in D. The present paper derives parameters at which psi attains its infimum and supremum on a given Gamma subset of Omega or takes their approximate values, This is achieved by using majorization methods. The results are applied to robust testing of several location parameters.