Author

Yan-Peng Li

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Preprint Oct 2026

When is Hotelling's $T^2$ asymptotically $F$-distributed?

For Gaussian observations, a deterministic multiple of Hotelling's $T^2$ statistic has an exact $F$ distribution. This paper investigates when this approximation remains valid for an independent and identically distributed (i.i.d.) data matrix $\mathbf{X}\in \mathbb{R}^{p\times n}$ with a fixed, possibly heavy-tailed e...

Yan-Peng Li, Guang-Ming Pan, Wang Zhou · 0 citations

Preprint Oct 2026

Staircase phase transitions for the largest eigenvalue of heavy-tailed sample correlation matrices

We establish staircase phase transitions for the largest eigenvalue of heavy-tailed sample correlation matrices formed from a $p_n \times n$ data matrix with i.i.d. real entries of mean zero and unit variance, allowing an infinite fourth moment. In the proportional regime $p_n / n \to \phi \in (0, \infty)$, the first-o...

Yan-Peng Li, Ze-Qin Lin, Yi-Ming Liu et al. · 0 citations