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

Guo Dong Xing, Shan Chao Yang, Xiaohu Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for α-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.

Original languageEnglish
Pages (from-to)416-430
Number of pages15
JournalCommunications in Statistics: Simulation and Computation
Volume48
Issue number2
DOIs
StatePublished - 7 Feb 2019

Keywords

  • Berry-Esseen bound
  • Frequency polygons
  • Uniformly Strong consistency
  • α-mixing

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