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In this paper, some asymptotic results such as weak consistency, strong consistency, uniformly strong consistency and the corresponding rates for the nearest neighbour estimator of the density function are established under  α -mixing samples. The results improve and extend some previous ones in the literature. As applications, the corresponding results on the consistencies for the estimator of the failure rate function in reliability theory are presented.

Consistency properties for the nearest neighbour estimator of the density function and applications based on α -mixing samples