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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xin Liu & Yi Wu & Wei Wang & Yong Zhu, 2023. "On Consistency of the Nearest Neighbor Estimator of the Density Function for m -AANA Samples," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4391-:d:1265100
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