On some properties of the Moran index

Abstract

The Moran index which is often used to detect spatial autocorrelation among geographical data in the main focus of this paper. In this article, we will derive exact and simple expression for the corresponding moments when the vector of observations is from a multivariate exchangeable population. We will also derive the distribution function of some ratios of quadratic forms, which like the Moran index are function of commuting matrices.