ALNQD序列密度函数核估计的强相合性

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 f n (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.