Asymptotic normality of recursive density estimates under some dependence assumptions

Let {X <Subscript> n </Subscript>,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 [InlineMediaObject not available: see fulltext.] where h <Subscript> n </Subscript> 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 <Subscript> n </Subscript>(x). Copyright Springer-Verlag 2004