混合序列密度函数核估计的相合性

Consistency of the Kernel Estimator of the Density Function for Mixing Random Variables Sequence

设{X_n,n≥1}是一随机变量序列,f(x)为其概率密度函数,基于样本X_1,X_2,…,X_n,对密度函数f(x)的核估计进行讨论,在适当条件下,利用Borel-Cantelli引理、矩不等式等证明了ρ-混合和φ混合序列核密度估计的强相合性、r阶相合性.

Let{ Xn, n ≥ 1 { be a random variables sequence, f（x） is the probability density function, the density kernel estimator of f（x） is discussed based on X1, X2,..., Xn, and the strong consistency and the r-order consistency of ρ- mixing and φ mixing random variables sequences are proved by Borel-Cantelli lemma and the moment inequalities under suitable conditions.