The Berry–Esseen bound for $\rho$-mixing random variables and its applications in nonparametric regression model

X. J. Wang   ; S. H. Hu

Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 584-608

Résumé

In this paper, the Berry–Esseen bound for $\rho$-mixing random variables with the rate of normal approximation $O(n^{-1/6}\log n)$ is established under some suitable conditions. By using the Berry–Esseen bound, we further investigate the Berry–Esseen bound of sample quantiles for $\rho$-mixing random variables. The rate of normal approximation is shown to be $O(n^{-1/6}\log n)$ under some suitable conditions. In addition, the asymptotic normality of the linear weighted estimator for the nonparametric regression model based on $\rho$-mixing errors is studied by using the Berry–Esseen bound that we established. Some new results are obtained in the paper under much weaker dependent structures.

Détail

Keywords: Berry–Esseen bound, normal approximation, nonparametric regression model, $\rho$-mixing sequence.
Mots-clés : sample quantiles

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