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An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation

Author

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  • Jiecheng Wang

    (Department of Statistics, School of Economics, Anhui University, Hefei 230039, China)

  • Yantong Liu

    (School of Management, North China University of Science and Technology, Tangshan 063210, China)

  • Jincai Chang

    (School of Science, North China University of Science and Technology, Tangshan 063210, China)

Abstract

There are three main problems for classical kernel density estimation in its application: boundary problem, over-smoothing problem of high (low)-density region and low-efficiency problem of large samples. A new improved model of multivariate adaptive binned quasi-interpolation density estimation based on a quadtree algorithm and quasi-interpolation is proposed, which can avoid the deficiency in the classical kernel density estimation model and improve the precision of the model. The model is constructed in three steps. Firstly, the binned threshold is set from the three dimensions of sample number, width of bins and kurtosis, and the bounded domain is adaptively partitioned into several non-intersecting bins (intervals) by using the iteration idea from the quadtree algorithm. Then, based on the good properties of the quasi-interpolation, the kernel functions of the density estimation model are constructed by introducing the theory of quasi-interpolation. Finally, the binned coefficients of the density estimation model are constructed by using the idea of frequency replacing probability. Simulation of the Monte Carlo method shows that the proposed non-parametric model can effectively solve the three shortcomings of the classical kernel density estimation model and significantly improve the prediction accuracy and calculation efficiency of the density function for large samples.

Suggested Citation

  • Jiecheng Wang & Yantong Liu & Jincai Chang, 2022. "An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2402-:d:858749
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    References listed on IDEAS

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    1. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    2. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    3. Shunpu Zhang & Rohana Karunamuni, 2010. "Boundary performance of the beta kernel estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 81-104.
    4. K. F. Cheng & C. K. Chu & Dennis K. J. Lin, 2006. "Quick multivariate kernel density estimation for massive data sets," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(5‐6), pages 533-546, September.
    5. Hall, Peter & Wand, M. P., 1996. "On the Accuracy of Binned Kernel Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 165-184, February.
    6. Weiran Lin & Qiuqin He, 2021. "The Influence of Potential Infection on the Relationship between Temperature and Confirmed Cases of COVID-19 in China," Sustainability, MDPI, vol. 13(15), pages 1-11, July.
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    Cited by:

    1. Jenny Farmer & Eve Allen & Donald J. Jacobs, 2022. "Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities," Mathematics, MDPI, vol. 11(1), pages 1-19, December.

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