Multimatricvariate and multimatrix variate distributions based on elliptically contoured laws under real normed division algebras

TL;DR

This paper introduces new families of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws within real normed division algebras, enabling advanced modeling of dependent random matrices and vectors.

Contribution

It develops novel distribution families for dependent random matrices and vectors in real normed division algebras, extending copula approaches with new inference capabilities.

Findings

Provides a framework for modeling dependent random matrices and vectors.

Defines likelihood functions for dependent samples in algebraic contexts.

Includes an application to quaternionic algebra with shape theory data.

Abstract

This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about random matrix variate distributions: 1) Modeling of two or more probabilistically dependent random variables in all possible combinations whether univariate, vector and matrix simultaneously. 2) Expected marginal distributions under independence and joint estimation of models under likelihood functions of dependent samples. 3) Definition of a likelihood function for dependent samples in the mentioned random dimensions and under real normed division algebras. The corresponding real distributions are alternative approaches to the existing univariate and vector variate copulas, with the additional advantages previously listed. An application for quaternionic algebra is illustrated by a computable dependent sample joint distribution for landmark data emerged from shape theory.