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The $$\beta $$ β -divergence for Bandwidth Selection in Circular Kernel Density Estimation

Author

Listed:
  • Babacar Diakhate

    (Université Cheikh Anta Diop)

  • Hamza Dhaker

    (Université de Moncton)

  • Papa Ngom

    (Université Cheikh Anta Diop)

Abstract

The choice of bandwidth is crucial in circular kernel density estimation. Various bandwidth selection techniques have been proposed in the literature. New bandwidth selectors based on the measure $$\beta $$ β -divergence for kernel density estimation with circular data are presented in this work. These selectors are obtained by minimizing the mean of the measure $$\beta $$ β -divergence between the density to be estimated and its estimator. The idea is based on the generalization of the standard method which selects the bandwidth by minimizing the mean integrated squared error (MISE). The performance of the proposed selectors is evaluated through a simulation study and compared with other existing selectors. These selectors are illustrated with some real datasets.

Suggested Citation

  • Babacar Diakhate & Hamza Dhaker & Papa Ngom, 2024. "The $$\beta $$ β -divergence for Bandwidth Selection in Circular Kernel Density Estimation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 417-437, September.
    • Handle: RePEc:spr:jagbes:v:29:y:2024:i:3:d:10.1007_s13253-023-00572-z
    DOI: 10.1007/s13253-023-00572-z
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    References listed on IDEAS

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    1. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    2. Di Marzio, Marco & Panzera, Agnese & Taylor, Charles C., 2009. "Local polynomial regression for circular predictors," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2066-2075, October.
    3. Agostinelli, Claudio, 2007. "Robust estimation for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5867-5875, August.
    4. 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.
    5. Abohela, Islam & Hamza, Neveen & Dudek, Steven, 2013. "Effect of roof shape, wind direction, building height and urban configuration on the energy yield and positioning of roof mounted wind turbines," Renewable Energy, Elsevier, vol. 50(C), pages 1106-1118.
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