NQD样本下密度函数核估计的相合性

Consistency of the kernel estimator of the density function for pairwise negative quadrant dependent sequences

设{Xn,n≥1}为同分布的两两NQD随机变量序列,f(x)为其概率密度函数,基于样本X1,X2,…,Xn,文章对密度函数f(x)的核估计进行了讨论,在适当条件下证明了强相合、一致强相合和均方相合。

Let {Xn,n≥} be a sequence of pairwise negative quadrant dependent（NQD） variables with the probability density function f（x）. Based on the NQD samples, the kernel estimator of f（x） is constructed,and strong consistency, uniformly strong consistency and square consistency are shown under suitable conditions.