m相依样本概率密度函数核估计的相合性

Consistency for the Kernel-type Density Estimator in the Case of m-Dependent Samples

设{Xn,n≥1}为严平稳的m相依随机变量序列,f(x)为X1的概率密度函数,基于样本X1,X2,…,Xn,构造了密度函数f(x)的核估计,并利用独立同分布样本的性质证明了f(x)核估计的r阶平均相合、逐点相合和一致强相合性.

Let {X,, n ≥ 1} be a strict stationary sequence of m-dependent random variables with probability density function f（x）. Based on m-dependent samples, the kernel estimator forf（x） is constructed, and with the application of the property of i. i. d. samples, the consistency in r-order mean, the pointwise strong consistency and strong uniform consistency are shown under suitable conditions.