Performance of the EM Algorithm on the Identification of a Mixture of Watson Distributions Defined on the Hypersphere

Abstract

We consider a set of n individuals described by p standardised variables, and we suppose that the individuals are previously selected from a population and the variables are a sample of variables assumed to come from a mixture of k bipolar Watson distributions defined on the hypersphere. In this context we provide the identification of the mixture through the EM algorithm and we also carry out a simulation study to compare the maximum likelihood estimates obtained from samples of moderate size with the respective asymptotic estimates. Our simulation results revealed good performance of the EM algorithm for moderate sample sizes.