a LS-CREST and UPRESA 8088, Université Cergy Pontoise, 95302, Cergy-Pontoise cedex, France;b Laboratoire GRESE, ENGREF, 75732, Paris cedex 15, France;c Vilnius Institute of Mathematics and Informatics, 2600, Vilnius, Lithuania
Abstract:
We discuss the asymptotic behavior of weighted empirical processes of stationary linear random fields in with long-range dependence. It is shown that an appropriately standardized empirical process converges weakly in the uniform-topology to a degenerated process of the form fZ, where Z is a standard normal random variable and f is the marginal probability density of the underlying random field.