两类相依样本密度函数核估计的相合性  

Consistency of Kernel-Type Density Estimations of Two Sorts of Dependent Samples

作　　者：胡学平[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246133

出　　处：《吉林大学学报（理学版）》2013年第6期1085-1089,共5页Journal of Jilin University:Science Edition

基　　金：安徽省高校自然科学基金重点项目(批准号:KJ2013A179;KJ2012Z233)

摘　　要：设{Xn,n≥1}为同分布的NOD随机序列或严平稳的m相依序列,f(x)为随机变量X1的概率密度函数.基于样本X1,X2,…,Xn,利用Fourier变换及NOD列的性质和相关指数不等式,研究密度函数f(x)的核估计,在适当的条件下得到了f(x)核估计的逐点强相合性、r阶相合性及依概率一致收敛性.Let { Xn,n≥ 1 } be an identically distributed NOD random sequence or a strict stationary sequence of m dependent random variables,and f（r） is a probability density function of random variable X1.Based on NOD samples or m dependent samples,under suitable conditions the kernel estimator for density function f（x） was investigated,and the pointwise strong consistency,the consistency in r order mean and uniform consistency in L1 were obtained via Fourier transform,the related properties for NOD random sequences and the exponential inequality.

关 键 词：NOD样本 M相依样本 核估计 强相合性 r阶相合性 

分 类 号：O212.2[理学—概率论与数理统计]