$\mathrm{L}_\infty$-Bound for Asymptotic Normality of Weakly Dependent Summands Using Stein's Result

Takahata, Hiroshi

Ann. Probab., Tome 9 (1981) no. 6, p. 676-683 / Harvested from Project Euclid

Résumé

Let $\{X_n\}$ be a strictly stationary process satisfying some mixing conditions, including $\phi$-mixing condition. It is the aim of the present paper to give, using a slight modification of Stein's result, a rate $O(n^{-1/2} \log n)$ of the normal approximation for a sum $S_n = X_1 + \cdots + X_n$.

Publié le : 1981-08-14
Classification: Stationary process, mixing, rate of the normal approximation, 60F05, 60G10

@article{1176994375,
     author = {Takahata, Hiroshi},
     title = {$\mathrm{L}\_\infty$-Bound for Asymptotic Normality of Weakly Dependent Summands Using Stein's Result},
     journal = {Ann. Probab.},
     volume = {9},
     number = {6},
     year = {1981},
     pages = { 676-683},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994375}
}

Takahata, Hiroshi. $\mathrm{L}_\infty$-Bound for Asymptotic Normality of Weakly Dependent Summands Using Stein's Result. Ann. Probab., Tome 9 (1981) no. 6, pp.  676-683. http://gdmltest.u-ga.fr/item/1176994375/