The consistency of the nearest neighbor estimator of the density function based on WOD samples

In this paper, the consistency of the nearest neighbor estimator of the density function based on widely orthant dependent (WOD, in short) samples is investigated. The convergence rate of strong consistency, the complete consistency, the uniformly complete consistency and uniformly strong consistency of the nearest neighbor estimator of the density function based on WOD samples are established. Our results established in the paper generalize or improve the corresponding ones for independent samples and some negatively dependent samples.