Let {Xn, n ≥ 1} be a strictly stationary sequence of negatively associated random variables, with common distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) for fixed k ∈ IN based on kernel type estimators. We introduce asymptotic normality and properties and moments. From these we derive the optimal bandwidth convergence rate, which is of order n−1. Besides of some usual conditions on the kernel function, the conditions typically impose a convenient increase rate on the covariances Cov(X1,Xn).

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