On Consistency of the Nearest Neighbor Estimator of the Density Function for m -AANA Samples

Xin Liu, Yi Wu, Wei Wang and Yong Zhu ()
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Xin Liu: Center of Applied Mathematics, School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China
Yi Wu: Center of Applied Mathematics, School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China
Wei Wang: Center of Applied Mathematics, School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China
Yong Zhu: Center of Applied Mathematics, School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China

Mathematics, 2023, vol. 11, issue 20, 1-17

Abstract: In this paper, by establishing a Bernstein inequality for m -asymptotically almost negatively associated random variables, some results on consistency for the nearest neighbor estimator of the density function are further established. The results generalize some existing ones in the literature. Some numerical simulations are also provided to support the results.

Keywords: nearest neighbor estimator; weak consistency; m -asymptotically almost negatively associated samples; strong consistency; uniform consistency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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