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An adaptive method for bandwidth selection in circular kernel density estimation

Author

Listed:
  • Stanislav Zámečník

    (Masaryk University)

  • Ivana Horová

    (Masaryk University)

  • Stanislav Katina

    (Masaryk University
    Institute of Computer Science of the Czech Academy of Sciences)

  • Kamila Hasilová

    (University of Defence)

Abstract

Kernel density estimations of circular data are an effective type of nonparametric estimation. The performance of these estimations depends significantly on a smoothing parameter referred to as bandwidth. Selecting suitable bandwidths for these types of estimation pose fundamental challenges, therefore fixed bandwidth selectors are often the initial choice. The study investigates common bandwidth selection methods and proposes novel methods which adopt the idea from the linear case. The attention is also paid to variable bandwidth selection. Using simulations which incorporate a range of circular distributions that exhibit multimodality, peakedness and skewness, the proposed methods were evaluated and then compared with other bandwidth selectors to determine their potential advantages. Two real datasets, one containing animal movements and the other wind direction data, were applied to illustrate the utility of the proposed methods.

Suggested Citation

  • Stanislav Zámečník & Ivana Horová & Stanislav Katina & Kamila Hasilová, 2024. "An adaptive method for bandwidth selection in circular kernel density estimation," Computational Statistics, Springer, vol. 39(4), pages 1709-1728, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01401-0
    DOI: 10.1007/s00180-023-01401-0
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    References listed on IDEAS

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    1. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    2. Di Marzio, Marco & Fensore, Stefania & Panzera, Agnese & Taylor, Charles C., 2019. "Kernel density classification for spherical data," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 23-29.
    3. Tsuruta, Yasuhito & Sagae, Masahiko, 2017. "Higher order kernel density estimation on the circle," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 46-50.
    4. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    5. Pham Ngoc, Thanh Mai, 2019. "Adaptive optimal kernel density estimation for directional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 248-267.
    6. Kanti V. Mardia, 2021. "Comments on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 59-63, March.
    7. Carlos Tenreiro, 2022. "Kernel density estimation for circular data: a Fourier series-based plug-in approach for bandwidth selection," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 34(2), pages 377-406, April.
    8. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
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