Uniformly strong consistency and Berry-Esseen bound of frequency polygons for α-mixing samples

摘要

In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for alpha-mixing samples. By some known exponent and moment inequalities, we obtain the uniformly strong consistency and Berry-Esseen bound of the estimator. The present results relax the relevant conditions used by Carbon et al. Furthermore, the convergence rate of the uniformly asymptotic normality is derived, which is O(n(- 1/11)) under the given conditions.