Berry-Esseen bounds for smooth estimator of a distribution function under association

Let (X-n; n greater than or equal to 1) be real-valued random variables forming a stationary sequence, and satisfying the basic requirement of being positively or negatively associated. Let F be the marginal distribution function of the X(i)s, which is estimated by a smooth kernel-type estimate <(F)over cap(>n), by means of the segment X-1,...,X-n. The main result of this paper is that of providing, under certain regularity conditions, Berry-Esseen bounds for the smooth estimator (F) over cap(n), thereby providing asymptotic normality of root n[(F) over cap(n)(x) - E((F) over cap(n)(x))] with rates.