Approximate null distribution of the largest root in multivariate analysis

TL;DR

This paper introduces a simple approximation for the null distribution of the largest root in multivariate analysis using the Tracy--Widom distribution, enabling easier initial screening without extensive tables or software.

Contribution

It proposes a novel approximation method for the largest root distribution, simplifying calculations in multivariate analysis.

Findings

The Tracy--Widom approximation is effective in many cases.

The approximation reduces reliance on extensive tables or software.

Illustrations demonstrate practical applicability.

Abstract

The greatest root distribution occurs everywhere in classical multivariate analysis, but even under the null hypothesis the exact distribution has required extensive tables or special purpose software. We describe a simple approximation, based on the Tracy--Widom distribution, that in many cases can be used instead of tables or software, at least for initial screening. The quality of approximation is studied, and its use illustrated in a variety of setttings.