Title: Elliptical symmetry models and robust estimation methods on spheres
Authors: Janice Scealy - Australian National University (Australia) [presenting]
Andrew Wood - The University of Nottingham (United Kingdom)
Abstract: First, a new distribution is proposed for analysing directional data that is a novel transformation of the von Mises-Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalising constant in the new density is easy to compute an estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter which controls the tail-weight of the distribution. Next, we define a more general semi-parametric elliptical symmetry model on the sphere and propose two new robust direction estimators, both of which are analogous to the affine-equivariant spatial median in Euclidean space. We calculate influence functions and show that the new direction estimators are standardised bias robust in the highly concentrated case. To illustrate our new models and estimation methods, we analyse archaeomagnetic data and lava flow data from two recently compiled online geophysics databases.