| Título: | Cram'er Type Moderate deviations for the Maximum of Self-normalized Sums |
| Autores: |
Hu, Zhishui; USTC Shao, Qi-Man; HKUST Wang, Qiying; University of Sydney |
| Fecha: | 2009-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Large deviation, moderate deviation, self-normalized maximal sum 60F10, 62E20 |
| Descripción: | Let $\{ X, X_i , i \geq 1\}$ be i.i.d. random variables, $S_k$ be the partial sum and $V_n^2 = \sum_{1\leq i\leq n} X_i^2$. Assume that $E(X)=0$ and $E(X^4) < \infty$. In this paper we discuss the moderate deviations of the maximum of the self-normalized sums. In particular, we prove that $P(\max_{1 \leq k \leq n} S_k \geq x V_n) / (1- \Phi(x)) \to 2$ uniformly in $x \in [0, o(n^{1/6}))$. |
| Idioma: | No aplica |
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