Asymptotics of kernel density estimators on weakly associated random fields

摘要

Let Z(N),N>=1 denote the integer lattice points in the N-dimensional Euclidean space and{X-n}be an R-d-valued,strictly stationary,weakly associated random field indexed by Z(N).Under mild conditions,as in [Roussas,G.G.,2000. Asymptotic normality of the kernel estimate of a probability density function under association. Statist.Probab.Lett. 50,1-12],asymptotic normality of the kernel estimator of the multivariate density is established.We also investigate the mean Squared error of the estimator towards the unknown density