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

Zhengliang Lu, Shengnan Ding, Fei Zhang, Rui Wang and Xuejun Wang

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 3, 669-684

Abstract: 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.

Date: 2022
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DOI: 10.1080/03610926.2020.1752727

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