On Consistency of the Nearest Neighbor Estimator of the Density Function and Its Applications

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In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency, strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.