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Weighted Probability Density Estimator with Updated Bandwidths

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Abstract

In this paper, the authors study a class of weighted version of probability density estimator. It is shown that the weighted estimator contains some existing estimators of probability density, no matter they are recursive or non-recursive. Some statistical results including weak consistency, strong consistency, rate of strong consistency, and asymptotic normality are established under some mild conditions. Moreover, the random weighted estimator is also investigated. Some numerical simulations and a real data analysis are presented to study the numerical performances of the estimators.

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Authors and Affiliations

  1. School of Big Data and Artificial Intelligence, Chizhou University, Chizhou, 247000, China

    Yi Wu

  2. School of Big Data and Statistics, Anhui University, Hefei, 230601, China

    Wei Yu & Xuejun Wang

  3. CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad, 500046, India

    B. L. S. Prakasa Rao

Authors
  1. Yi Wu
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  2. Wei Yu
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  3. Xuejun Wang
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  4. B. L. S. Prakasa Rao
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Corresponding author

Correspondence to Xuejun Wang.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 12201079, 12201004, and 11871072, the National Social Science Foundation of China under Grant No. 22BTJ059, the Natural Science Foundation of Anhui Province under Grant Nos. 2108085QA15 and 2108085MA06, and the “INSA Senior Scientist” scheme at the CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad 500046, India.

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Wu, Y., Yu, W., Wang, X. et al. Weighted Probability Density Estimator with Updated Bandwidths. J Syst Sci Complex 37, 886–906 (2024). https://doi.org/10.1007/s11424-024-2054-2

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  • DOI: https://doi.org/10.1007/s11424-024-2054-2

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