%0 Journal Article
%T WOD样本下密度函数核估计的收敛性<br>Convergence properties of the kernel-type density estimator under WOD dependent samples
%A 胡学平
%A 张红梅&lt
%A br&gt
%A HU Xue-ping
%A ZHANG Hong-mei
%J 山东大学学报（理学版）
%D 2017
%R 10.6040/j.issn.1671-9352.0.2016.329
%X 摘要： 设{Xn,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。<br>Abstract: Let {Xn,n≥1} 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 density 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
%K WOD样本&lt
%K i&gt
%K &lt
%K /i&gt
%K 密度函数核估计&lt
%K i&gt
%K &lt
%K /i&gt
%K 逐点强相合性
%K r &lt
%K /i&gt
%K 阶相合性&lt
%K i&gt
%K &lt
%K br&gt
%K WOD samples
%K consistency in &lt
%K i&gt
%K r&lt
%K /i&gt
%K order mean
%K kernel estimator
%K pointwise strong consistency
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2016.329