WOD样本下密度函数核估计的收敛性  

Convergence properties of the kernel-type density estimator under WOD dependent samples

作　　者：胡学平 张红梅 HU Xue-ping ZHANG Hong-mei(School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, Anhui, China)

机构地区：[1]安庆师范大学数学与计算科学学院,安徽安庆246133

出　　处：《山东大学学报（理学版）》2017年第4期21-25,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金数学天元专项基金资助项目(11626031);安徽省高校自然科学基金重点项目(KJ2013A179)

摘　　要：设{X_n,n≥1}为同分布的WOD随机序列,f(x)为共同的概率密度函数。利用WOD序列的Rosenthal-型矩不等式和Bernstein-型指数不等式,对密度函数f(x)的核估计进行了探讨,在适当条件下得到了核估计的r阶相合性、逐点强相合性和依概率一致收敛性。Let {Xn,n≥1} t be an identically distributed WOD random sequence with a commen density functiong f（x）. Based on the Rosenthal-type inequality and Bernstein-type inequality for WOD sequence, the kernel estimator for densi- ty function f（x） was investigated under suitable conditions, and the consistency in r order mean, the pointwise strong consistency and uniform consistency in L1 were obtained.

关 键 词：WOD样本 密度函数核估计 r阶相合性 逐点强相合性 

分 类 号：O212[理学—概率论与数理统计]