负相协样本分布函数的递归型核估计

A Recursive Distribution Function Estimator Under NA Samples

设{Xn;n≥1}是一实值平稳负相协具有相同未知分布函数F(x)的随机变量序列,本文给出了F(x)一种递归型核估计F∧n(x)=1nj∑=n1K(x-hjXj),并讨论了它的渐近正态性,这里K(.)是已知的分布函数,窗宽{hj}满足hj↓0(j→+∞)。

Let{ Xn; n≥ 1 } be a strictly stationary sequence, and satisfying the basic requirement of being negatively asso-ciated, let F（x） be the marginal distribution function of {Xn}, which is estimated by the recursive kerneltype estimate ^∧Fn（x）=1/n∑^nj=n1K（x-Xj/hj） , Where bandwidthshj↓0 as j→＋∞, kernel function K（·）is a known distribution function. In tiffs paper, we discuss the point asymptotic normality for ^∧Fn（x） under certain regularity conditions.