摘要：Let $\mathbf{X}, \mathbf{X}_1, \mathbf{X}_2, ...$ be i.i.d. $\mathbb{R}^d$-valued random variables. We prove large and moderate deviations for Hotelling's $T^2$-statistic when $\mathbf{X}$ is in the generalized domain of attraction of the normal law.
关键词：large deviation; moderate deviation; self-normalized partial sums; law of the iterated logarithm; $T^2$ statistic;Primary 60F10, 60F15 ; Secondary 62E20, 60G50
