Shape Theory Via SV Decomposition II

TL;DR

This paper extends shape theory by deriving non-isotropic elliptical shape distributions using SVD decomposition, applying invariant and zonal polynomials, and demonstrating their use in biological data analysis with model selection.

Contribution

It introduces generalized elliptical shape distributions via SVD, expanding previous models and applying them to real biological data with a novel BIC-based model selection method.

Findings

Derived new elliptical shape distributions using SVD

Applied models to biological data successfully

Used modified BIC for optimal model selection

Abstract

The non isotropic and non central elliptical shape distributions via the Le and Kendall SVD decomposition approach are derived in this paper in the context of invariant polynomials and zonal polynomials. The so termed cone and disk densities here obtained generalise some results of the literature. Finally, some particular densities are applied in a classical data of Biology, and the inference is performed after choosing the best model by using a modified BIC criterion.