A stereographic projection method for tests of equal mean direction in R n

Abstract

Statistical tests involving mean directions have in the past been limited to 2 and 3 dimensional settings, perhaps due to their primary applications to such fields as geology, meteorology, and related earth sciences. In the study of interactive multicriteria optimization, it is necessary to compare gradient directions obtained from decision makers by various methods. Quite often direction vectors are in a higher dimensional space. This paper provides a general procedure, based on Householder transformations, which is suitable for any finite dimension.