渐近负相依随机样本下边缘频率多边形估计的渐近正态性

胡学平; 王子予

doi:10.1051/wujns/2026315459

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渐近负相依随机样本下边缘频率多边形估计的渐近正态性

Mathematics | 更新时间：2026-10-29

- 渐近负相依随机样本下边缘频率多边形估计的渐近正态性
- Asymptotic Normality for the Edge Frequency Polygons under Asymptotically Negatively Associated Samples
- 武汉大学学报自然科学英文版 2026年31卷第5期页码：459-470
- 作者机构：
  
  安庆师范大学数学与统计学院, 安徽安庆 246133
- 作者简介：
  
  HU Xueping, male, Professor, research direction: nonparametric large sample theory. E-mail: hxprob@163.com
- 基金信息：
  
  the National Social Science Foundation of China(21BTJ040)
- DOI：10.1051/wujns/2026315459
  中图分类号： O212.7
- 收稿：2025-11-13，
  
  纸质出版：2026-10-24
- 稿件说明：
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胡学平,王子予.渐近负相依随机样本下边缘频率多边形估计的渐近正态性[J].武汉大学学报自然科学英文版,2026,31(05):459-470.

HU Xueping, WANG Ziyu. Asymptotic Normality for the Edge Frequency Polygons under Asymptotically Negatively Associated Samples[J]. Wuhan Univ J of Nat Sci, 2026, 31(5): 459-470.
胡学平,王子予.渐近负相依随机样本下边缘频率多边形估计的渐近正态性[J].武汉大学学报自然科学英文版,2026,31(05):459-470. DOI： 10.1051/wujns/2026315459.

HU Xueping, WANG Ziyu. Asymptotic Normality for the Edge Frequency Polygons under Asymptotically Negatively Associated Samples[J]. Wuhan Univ J of Nat Sci, 2026, 31(5): 459-470. DOI： 10.1051/wujns/2026315459.

摘要

基于直方图技术的边缘频率多边形估计，其收敛速度与非负核估计相当，且具有计算简便的优势。本文在合适的条件下，探讨了基于渐近负相依（ANA）随机序列的边缘频率多边形估计的一致渐近正态性，获得其收敛速度近似于

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275231&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275206&type=

11.99444389

4.23333359

，表明了该估计具有与核估计类似的Berry-Esséen界。此外，通过数值模拟验证了上述理论结果。

Abstract

The edge frequency polygon estimator

which is based on the histogram technique

has a convergence rate similar to that of the nonnegative kernel estimator and possesses the advantage of computational simplicity. In this paper

the uniformly asymptotic normality of the edge frequency polygon estimator for asymptotically negatively associated (ANA) random variables is established under suitable conditions

and the convergence rate is approximately

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275215&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275227&type=

10.30111122

3.80999994

which reveals that the edge frequency polygon estimator has a similar Berry-Esséen bound of the kernel estimator. Additionally

some numerical simulations are carried out to validate the theoretical results.

关键词

Keywords

references

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