On Berry–Esséen bound of frequency polygon estimation under $$\rho $$ -mixing samples

IF 0.9 4区 数学 Q3 STATISTICS & PROBABILITY
Metrika Pub Date : 2024-02-06 DOI:10.1007/s00184-023-00944-y
Yi Wu, Xuejun Wang
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引用次数: 0

Abstract

The frequency polygon estimation, which is based on histogram technique, has similar convergence rate as those of non-negative kernel estimators and the advantages of computational simplicity. This work will study the Berry–Esséen bound of frequency polygon estimation with \(\rho \)-mixing samples under some general conditions. The rates are shown to be \(O(n^{-1/9})\) if the mixing coefficients decay polynomially and \(O(n^{-1/6}\log ^{1/3}n)\) if the mixing coefficients decay geometrically. These results improve and extend the corresponding ones in the literature and reveal that the frequency polygon estimator also has similar Berry–Esséen bound as those of kernel estimators. Moreover, some numerical analysis is also presented to assess the finite sample performance of the theoretical results.

Abstract Image

论 $$rho $$ 混合样本下频率多边形估计的 Berry-Esséen 边界
基于直方图技术的频率多边形估计与非负核估计具有相似的收敛率和计算简单的优点。这项工作将研究在一些一般条件下,具有 \(\rho \)-混合样本的频率多边形估计的贝里-埃森边界。结果表明,如果混合系数多项式衰减,速率为(O(n^{-1/9});如果混合系数几何衰减,速率为(O(n^{-1/6}\log ^{1/3}n))。这些结果改进并扩展了文献中的相应结果,并揭示了频率多边形估计器也具有与核估计器相似的贝里-艾森约束。此外,还提出了一些数值分析来评估理论结果的有限样本性能。
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来源期刊
Metrika
Metrika 数学-统计学与概率论
CiteScore
1.50
自引率
14.30%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
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