A spherical correlation coefficient robust against scale

Abstract

There are several bidirectional situations where it is required to obtain a measure of correlation. The question has been raised often that the bidirectional correlation coefficients so far known are not scale invariant, even asymptotically in the sense that their asymptotic distributions under the hypothesis of independence with von Mises marginals depend upon concentration parameters. Following a conditional approach of Cox (1975), we introduce a new correlation coefficient which is asymptotically robust in this sense. We obtain its asymptotic distribution under the hypothesis of independence and examine its properties. A numerical example is also given