NA随机变量的递归密度核估计的渐近正态性

Asymptotic Normality of the Recursive Kernel Estimate of a Probability Density Function under Negatively Associated

摘要: 设X_n,n≥1为同分布的NA样本序列,其未知概率密度函数为f(x),基于样本X₁,…,X_n,用递归密度核估计 f_n(x)=\frac1n \sum_j=1^n \frac1h_j K\left(\fracx-X_jh_j\right) 对f(x)进行估计.本文研究了在一定条件下,f_n(x)的渐近正态性.

Abstract: Let X₁,… ,X_n be negatively associated （NA） random samples from an unknown density function f（x）. The recursive kernel density function estimator can be obtained by putting f_n(x)=\frac1n \sum_j=1^n h_j^-1 K\left(\fracx-X_jh_j\right). In the paper, we will discuss the asymptotic normality for density estimator f_n（x） under suitable condition.