ALNQD序列密度函数核估计的强相合性  

Strong Consistency of Kernel Estimator of Density Function for ALNQD Sequence

作　　者：陆冬梅[1] 

机构地区：[1]长春理工大学光电信息学院,长春130022

出　　处：《吉林大学学报（理学版）》2017年第6期1461-1464,共4页Journal of Jilin University:Science Edition

基　　金：吉林省自然科学基金(批准号:20170101061JC)

摘　　要：设{X_n,n≥1}为一同分布的渐近线性负相依(ALNQD)序列,f_n(x)为密度函数f(x)基于样本X_1,…,X_n的核估计.在适当的假设条件下,利用ALNQD序列的矩不等式和Borel-Cantelli引理,证明核密度估计的强相合性、一致强相合性及r阶相合性.Let {X_n,n≥1}be an asymptotically linear negative quadrant dependent（ALNQD）sequence with the same distribution,and fn（x）be the kernel estimator of the density function f（x）based on the sample X_1,…,X_n.Under some suitable assumptions,the author proved the strong consistency,the uniform strong consistency and the r-order consistency of the kernel density estimator by using the moment inequalities of ALNQD sequences and Borel-Cantelli lemma.

关 键 词：ALNQD序列 核估计 (一致)强相合性 r阶相合性 

分 类 号：O211.4[理学—概率论与数理统计]