Central limit theorem for Hotelling's $T^2$ statistic under large dimension

TL;DR

This paper establishes a central limit theorem for Hotelling's $T^2$ statistic in high-dimensional settings where the dimension grows proportionally with the sample size.

Contribution

It provides the first CLT result for Hotelling's $T^2$ in large-dimensional regimes with proportional growth.

Findings

CLT for Hotelling's $T^2$ under high-dimensional asymptotics

Dimension proportional to sample size considered

Theoretical foundation for high-dimensional multivariate analysis

Abstract

In this paper we prove the central limit theorem for Hotelling's $T^2$ statistic when the dimension of the random vectors is proportional to the sample size.