The consistency and convergence rate for the nearest neighbor density estimator based on φ-mixing random samples.

In this work, we mainly investigate the consistency and strong convergence rate for the nearest neighbor density estimator based on φ -mixing random samples. The weak consistency, complete consistency, the rates of complete consistency and strong consistency for the nearest neighbor estimator of density function based on φ -mixing random samples are established. The results obtained in the article extend some corresponding ones for independent samples. [ABSTRACT FROM AUTHOR]