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

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.