Estimation of the mean measure density of a discrete random measure through associated sequences of observations

To estimate the density f of the mean measure of a discrete random measure eta, the sequence (eta(n))(n is an element of N) of the observed random measures is usually supposed to be independent. In this paper, that sequence is associated: this definition is a particular case of association of probability measure on a partially ordered Polish space (Lindqvist) [18]). The kernel estimator of f converges in probability and almost surely, pointwise and uniformly, under second-order moment conditions on eta(n) and on the sequence (h(n)) of the window-widths of the estimator.