## 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.