Asymptotic Normality for the Edge Frequency Polygons under Asymptotically Negatively Associated Samples

HU Xueping; WANG Ziyu

doi:10.1051/wujns/2026315459

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Asymptotic Normality for the Edge Frequency Polygons under Asymptotically Negatively Associated Samples

Mathematics | 更新时间：2026-10-29

- Asymptotic Normality for the Edge Frequency Polygons under Asymptotically Negatively Associated Samples
- Wuhan University Journal of Natural Sciences Vol. 31, Issue 5, Pages: 459-470(2026)
- 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：
- DOI：10.1051/wujns/2026315459
  CLC： O212.7
- Received：13 November 2025，
  
  Published：24 October 2026
- 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

Scott D W . Frequency polygons: Theory and application [J ] . Journal of the American Statistical Association , 1985 , 80 ( 390 ): 348 - 354 .

Jones M C , Samiuddin M , Al-Harbey A H , et al . The edge frequency polygon [J ] . Biometrika , 1998 , 85 ( 1 ): 235 - 239 .

Carbon M , Francq C , Tran L T . Asymptotic normality of frequency polygons for random fields [J ] . Journal of Statistical Planning and Inference , 2010 , 140 ( 2 ): 502 - 514 .

Yang X . Frequency polygon estimation of density function for dependent samples [J ] . Journal of the Korean Statistical Society , 2015 , 44 ( 4 ): 530 - 537 .

Xing G D , Yang S C , Liang X . On the uniform consistency of frequency polygons for ψ -mixing samples [J ] . Journal of the Korean Statistical Society , 2015 , 44 ( 2 ): 179 - 186 .

Wen Y Z , Xing G D . On the uniformly asymptotic normality of frequency polygons for ψ -mixing samples [J ] . Communications in Statistics—Theory and Methods , 2017 , 46 ( 21 ): 10416 - 10425 .

Xing G D , Yang S C . Uniformly strong consistency of frequency polygons for negatively associated samples [J ] . Communications in Statistics—Simulation and Computation , 2017 , 46 ( 3 ): 2168 - 2175 .

Xing G D , Yang S C , Li X H . Uniformly strong consistency and Berry-Esséen bound of frequency polygons for α -mixing samples [J ] . Communications in Statistics—Simulation and Computation , 2019 , 48 ( 2 ): 416 - 430 .

Kang S L , Abbasi R , Wang H L , et al . Asymptotic behaviour of frequency polygons under φ -mixing samples [J ] . Communications in Statistics—Theory and Methods , 2018 , 47 ( 21 ): 5369 - 5377 .

Xi M M , Wang C H , Wang X J . Uniformly strong consistency and the rates of asymptotic normality for the edge frequency polygons [J ] . Statistics , 2023 , 57 ( 6 ): 1444 - 1468 .

Younso A . Consistency of the frequency polygon estimators of density mode for strongly mixing processes [J ] . Communications in Statistics—Theory and Methods , 2023 , 52 ( 7 ): 2182 - 2197 .

Wu Y , Wang X J . On Berry-Esséen bound of frequency polygon estimation under ρ -mixing samples [J ] . Metrika , 2025 , 88 ( 1 ): 19 - 41 .

Wang W , Wang H , Wu Y . Consistency of the frequency polygon estimators of density function and density mode under m -END samples [J ] . Communications in Statistics—Theory and Methods , 2025 , 54 ( 5 ): 1271 - 1286 .

Chao X L , Hu X P . Asymptotic normality of the frequency polygon estimators under widely orthant dependent samples [J ] . Communications in Statistics—Simulation and Computation , 2026 , 55 ( 9 ): 3700 - 3717 .

Bradley R C . On the spectral density and asymptotic normality of weakly dependent random fields [J ] . Journal of Theoretical Probability , 1992 , 5 ( 2 ): 355 - 373 .

Zhang L X , Wang X Y . Convergence rates in the strong laws of asymptotically negatively associated random fields [J ] . Applied Mathematics—A Journal of Chinese Universities , Series B, 1999 , 14 ( 4 ): 406 - 416 .

Zhang L X . Central limit theorems for asymptotically negatively associated random fields [J ] . Acta Mathematica Sinica , 2000 , 16 ( 4 ): 691 - 710 .

Tang X F , Xi M M , Wu Y , et al . Asymptotic normality of a wavelet estimator for asymptotically negatively associated errors [J ] . Statistics & Probability Letters , 2018 , 140 : 191 - 201 .

Wu Y , Wang X J , Shen A T . Strong convergence properties for weighted sums of m -asymptotic negatively associated random variables and statistical applications [J ] . Statistical Papers , 2021 , 62 ( 5 ): 2169 - 2194 .

Petrov V V . Limit theorems of probability theory: Sequences of independent random variables [J ] . Proceedings of the Edinburgh Mathematical Society , 1996 , 39 ( 3 ): 591 - 592 .

Ledoux M , Talagrand M . Probability in Banach Spaces [M ] . Berlin, Heidelberg : Springer-Verlag , 1991 .

Yang S C . Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples [J ] . Statistics & Probability Letters , 2003 , 62 ( 2 ): 101 - 110 .

Joag-Dev K , Proschan F . Negative association of random variables with applications [J ] . The Annals of Statistics , 1983 , 11 ( 1 ): 286 - 295 .

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