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Estimation of a two-dimensional distribution function under association. (English) Zbl 1031.62027
Summary: By considering an associated and strictly stationary sequence of random variables, say \(X_n\), \(n\geqslant 1\), we study the properties of a histogram estimator for the two-dimensional distribution function of (\(X_1,X_{k+1}\)). 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. We also characterize the mean square error (MSE) and find its convergence rate, under assumptions on the convergence rate of the covariances.

MSC:
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
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