The consistency and convergence rate for the nearest neighbor density estimator based on \(\varphi\)-mixing random samples. (English) Zbl 07532298
Summary: In this work, we mainly investigate the consistency and strong convergence rate for the nearest neighbor density estimator based on \(\varphi\)-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 \(\varphi\)-mixing random samples are established. The results obtained in the article extend some corresponding ones for independent samples.
Keywords:
complete consistency; convergence rate; nearest neighbor estimator; strong consistency; \(\varphi\)-mixing random variables; weak consistencyReferences:
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