Generalised shape theory via SV decomposition I

Abstract

This work finds in terms of zonal polynomials, the non isotropic noncentral elliptical shape distributions via singular value decomposition; it avoids the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure is based on exact densities, instead of the published approximations and asymptotic distribution of isotropic models. An application of the technique is illustrated with a classical landmark data of Biology, for this, three Kotz type models are proposed (including Gaussian); then the best one is chosen by using a modified BIC criterion.