安庆师范大学学报（自然科学版）2026，Vol.32Issue(2)：28-32,5.DOI:10.13757/j.cnki.cn34-1328/n.2026.02.004
宽象限相依下密度估计的一致强相合性
Uniform Strong Consistency of Density Estimation for Widely Orthant Dependent Samples
摘要
Abstract
The interpolated frequency polygon estimator is an important method for probability density estimation.Its convergence rate is comparable to that of kernel density estimation but superior to that of histogram estimation,offering dis-tinct advantages in computational complexity and boundary treatment.This advantage is particularly evident in bivariate set-tings,where it facilitates the construction of exact equiprobable contours.Focusing on the theoretical properties of frequency polygon estimators in the context of dependent data,this paper establishes the theoretical properties of frequency polygon esti-mators under widely orthant dependent(WOD)sequences.Utilizing Bernstein-type exponential inequalities and truncation techniques,we derive the uniform strong consistency for both the density estimator and the associated failure rate function,a key metric in reliability analysis.Our results extend existing literature and reinforce the theoretical foundation of nonparamet-ric estimation for dependent samples.关键词
WOD/频率多边形/失效率函数/一致强相合性/密度估计Key words
WOD/frequency polygon/failure rate function/uniformly strong consistency/density estimation分类
数理科学引用本文复制引用
李会葆,潮学琳,阮景..宽象限相依下密度估计的一致强相合性[J].安庆师范大学学报（自然科学版）,2026,32(2):28-32,5.基金项目
大别山区域复杂生态系统建模、仿真与控制重点实验室项目(SLXY24A001),安徽省高等学校省级质量工程项目(2025zytsct029)和安庆师范大学校级质量工程项目(2024aqnujyxm07) （SLXY24A001）
