# A technical note on divergence of the Wald statistic

## TL;DR

This paper investigates the divergence behavior of the Wald test statistic, linking it to eigenvalues of polynomial matrices and establishing the rate of divergence under certain conditions.

## Contribution

It provides a mathematical connection between Wald statistic divergence and eigenvalues, and quantifies the divergence rate, enhancing understanding of Wald test limitations.

## Key findings

- Divergence of Wald statistic linked to eigenvalues
- Established divergence rate under specific conditions
- Provides theoretical insights into Wald test behavior

## Abstract

The Wald test statistic has been shown to diverge (Dufour et al, 2013, 2017) under some conditions. This note links the divergence to eigenvalues of a polynomial matrix and establishes the divergence rate.