Large and moderate deviations for Hotelling’s \(T^2\)-statistic. (English) Zbl 1112.60017

Dembo, Amir; Shao, Qi-Man

Electron. Commun. Probab. 11, 149-159 (2006).

Summary: Let \(X,X_1,X_2,\dots\) be i.i.d. \(\mathbb{R}^d\)-valued random variables. We prove large and moderate deviations for Hotelling’s \(T^2\)-statistic when \(X\) is in the generalized domain of attraction of the normal law.

MSC:

60F10	Large deviations
60F15	Strong limit theorems
60G50	Sums of independent random variables; random walks
62E20	Asymptotic distribution theory in statistics

Keywords:

large deviation; moderate deviation; self-normalized partial sums; law of the iterated logarithm