Sharp moderate deviations and uniform Berry--Esseen bounds for Hotelling's $T^2$-statistic via Stein's method

Song-Hao Liu, Qi-Man Shao, Hao Shi +1

Let ${\mathbf{X}}_1,\dots ,{\mathbf{X}}_n$ be independent random vectors in ${\mathbb{R}}^d$ with common mean ${\mathbf{\mu }}_n$, where $d\ge 2$ is a fixed integer. Let $\bar{\mathbf X}_n=n^{-…