Covariance estimator for associated random variables

Considering an associated and strictly stationary sequence of random variables we introduce an histogram estimator for the covariances between indicator functions of those random variables. We find conditions on the covariance structure of the original random variables for the almost sure convergence of the estimator and for the convergence in distribution of the finite dimensional distributions. Finally we characterize the usual error criteria finding their convergence rates under assumptions on the convergence rate of the covariances