This paper considers a moving average process for a sequence of negatively associated random variables. It discusses the complete convergence of such a moving average process under suitable conditions. These results generalize and complement earlier results on independent random variables. Also, a conjecture for the case of a sequence of independent and identically distributed random variables is resolved and its moment condition weakened.

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Based on the idea of the local polynomial smoother, we construct the Nadaraya-Watson type and local linear estimators of conditional density function for a left-truncation model. Asymptotic normality of the estimators is established under the lifetime observations are assumed to be a sequence of stationary α-mixing random variables. Finite sample behavior of the estimators is investigated via simulations too.