Multivariate Statistical Analysis: A Geometric Perspective

TL;DR

This paper introduces a geometric, coordinate-free approach to multivariate statistical analysis, utilizing tensor products and modules over matrix rings to develop classical statistical methods in a new framework.

Contribution

It presents a novel geometric framework for multivariate analysis, defining models and hypotheses without coordinates, and extends classical methods using tensor algebra.

Findings

Develops a coordinate-free geometric formulation of multivariate models

Defines statistical criteria for linear hypotheses in geometric terms

Establishes an analogy between classical and geometric multivariate analysis

Abstract

A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear hypotheses. As a result, multivariate statistical analysis is developed in full analogy to classical statistical analysis. This approach is based on tensor products and modules over the ring of square matrices, supplied with an inner product.