Shape Theory via QR decomposition

TL;DR

This paper introduces a new approach to shape theory using QR decomposition, enabling exact density computations for non-isotropic, noncentral elliptical shape distributions, with applications in biological data analysis.

Contribution

It develops a novel shape distribution framework via QR decomposition that avoids invariant polynomials, facilitating exact inference under complex elliptical models.

Findings

New shape distributions are easily computable.

Exact densities enable more precise inference.

Application demonstrated in biological data analysis.

Abstract

This work sets the non isotropic noncentral elliptical shape distributions via QR decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure can be studied under exact densities instead under the published approximations and asymptotic densities under isotropic models. An application in Biology is studied under the classical gaussian approach and a two non gaussian models.