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

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.