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A Bayesian procedure for bandwidth selection in circular kernel density estimation

Author

Listed:
  • Bedouhene Kahina

    (Department of Mathematics, Mouloud Mammeri University of Tizi-Ouzou, Tizi-Ouzou, Algeria)

  • Zougab Nabil

    (Department of Technology and Research Unit LaMOS, University of Bejaia, Bejaia, Algeria)

Abstract

A Bayesian procedure for bandwidth selection in kernel circular density estimation is investigated, when the Markov chain Monte Carlo (MCMC) sampling algorithm is utilized for Bayes estimates. Under the quadratic and entropy loss functions, the proposed method is evaluated through a simulation study and real data sets, which were already discussed in the literature. The proposed Bayesian approach is very competitive in comparison with the existing classical global methods, namely plug-in and cross-validation techniques.

Suggested Citation

  • Bedouhene Kahina & Zougab Nabil, 2020. "A Bayesian procedure for bandwidth selection in circular kernel density estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(1), pages 69-82, March.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:1:p:69-82:n:3
    DOI: 10.1515/mcma-2020-2056
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    References listed on IDEAS

    as
    1. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    2. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    3. Yasmina Ziane & Nabil Zougab & Smail Adjabi, 2018. "Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data," Computational Statistics, Springer, vol. 33(1), pages 299-318, March.
    4. 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.
    5. Oliveira, M. & Crujeiras, R.M. & Rodríguez-Casal, A., 2012. "A plug-in rule for bandwidth selection in circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3898-3908.
    6. Charles C. Taylor & Kanti V. Mardia & Marco Di Marzio & Agnese Panzera, 2012. "Validating protein structure using kernel density estimates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2379-2388, July.
    7. Tristan Senga Kiessé & Nabil Zougab & Célestin C. Kokonendji, 2016. "Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data," Computational Statistics, Springer, vol. 31(1), pages 189-206, March.
    8. Oliveira, María & Crujeiras, Rosa M. & Rodríguez-Casal, Alberto, 2014. "NPCirc: An R Package for Nonparametric Circular Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i09).
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