Asymptotic normality of the kernel estimate of a probability density function under association

Abstract

The sole purpose of this paper is to establish asymptotic normality of the usual kernel estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. In much of the discussions and derivations, the term association is used to include both positively and negatively associated random variables. The method of proof follows the familiar pattern for dependent situations of using large and small blocks. A result made available in the literature recently is instrumental in the derivations.