宽象限相依样本下频率插值密度估计的收敛性质  

Convergence Properties of Frequency Interpolation Density Estimation under Wide Orthant Dependent Samples

作　　者：潮学琳 胡学平 CHAO Xuelin;HU Xueping(School of Mathematics and Physics,Anqing Normal University,Anqing Anhui,246133)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《山西大同大学学报（自然科学版）》2024年第1期32-36,共5页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：省级研究生创新创业竞赛[2022cxcyjs027];省级研究生教育教学改革研究项目[2022jyjxggyj321]。

摘　　要：频率多边形插值估计是一种非常重要的概率密度估计方法,该估计不仅在相同计算量下比直方图估计收敛速度快,而且在计算二元数据集合比核密度估计更简单、便捷,所以对其进一步探究是有理论研究价值的。设{Xn,n≥1}为宽象限相依的随机序列,具有未知的密度函数f(x),利用宽象限相依序列的Rosenthal-型不等式和截尾的技术,在适当的条件情况下,获得了频率插值密度估计的强相合性和r阶矩相合性。Frequency polygon interpolation estimation is a very important probability density estimation method,which not only converges faster than histogram estimation under the same amount of calculation but also is simpler and more convenient than density kernel estimation in calculating binary metadata sets,so further exploration of it is valuable.Let{Xn,n≥1} be a wide orthant dependent sequence,with a common unknown density function f(x),by using the Rosenthal-type inequality for wide orthant dependent sequence and truncated technique,under the right conditions,the strong consistency and the r-order mean consistency of frequency interpolation density estimation are obtained.

关 键 词：宽象限相依序列 频率插值估计 强相合性 r阶收敛 

分 类 号：O211.4[理学—概率论与数理统计]