Asymptotic normality of recursive density estimates under some dependence assumptions

Abstract

Let {X n ,n≥1} be a strictly stationary sequence of negatively associated random variables with the marginal probability density function f(x), the recursive kernel estimate of f(x) is defined by where h n is a sequence of positive bandwidths tending to 0, as n→∞, K(·) is a univariate kernel function. In this note, we discuss the point asymptotic normality for f n (x).