George G. Roussas, University of California, Davis

Asymptotic Normality of Kernel Estimate Under Association

The concept of association is introduced briefly, and some areas, where it has found applications, are mentioned. Also, some results are listed, which have been obtained under the basic assumption of association. Then the problem is entertained of estimating the probability density function of random variables forming a discrete parameter stationary and associated stochastic process. The estimate considered is a kernel estimate. By utilizing results made available in the literature recently, the asymptotic normality of the kernel estimate is obtained. Also, an Esseen-type inequality for probability density functions is considered, and, as an application of it, one may establish consistency, in the probability sense, of the kernel estimate under consideration.