A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension

Abstract

We consider a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. To incorporate constraints imposed on the original model parameters, we propose a new parameterization of the distribution so that all new model parameters are free of constraints. Via the new parameterization, we translate the original problem of maximum likelihood estimation subject to complex constraints to a routine optimization problem free of constraints, which in turn leads to theoretically sound and numerically stable procedures for drawing likelihood-based inference. Byproducts from the likelihood-based inference are used to develop graphical and numerical diagnostic tools for assessing goodness of fit of this distribution in a data application. Simulation study and application to data from a hydrogeology study are used to demonstrate implementation and performance of the inference procedures and diagnostics methods.