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Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation

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  • Zougab, Nabil
  • Adjabi, Smail
  • Kokonendji, Célestin C.

Abstract

Bandwidth selection in multivariate kernel density estimation has received considerable attention. In addition to classical methods of bandwidth selection, such as plug-in and cross-validation methods, Bayesian approaches have also been previously investigated. Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation is investigated, when the quadratic and entropy loss functions are used. Under the quadratic loss function, the proposed method is evaluated through a simulation study and two real data sets, which were already discussed in the literature. For these real-data applications, very interesting advantages of the proposed method are pointed out.

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  • Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:28-38
    DOI: 10.1016/j.csda.2014.02.002
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    2. Célestin C. Kokonendji & Sobom M. Somé, 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics," Stats, MDPI, vol. 4(1), pages 1-22, March.
    3. Nan Yang & Yu Huang & Dengxu Hou & Songkai Liu & Di Ye & Bangtian Dong & Youping Fan, 2019. "Adaptive Nonparametric Kernel Density Estimation Approach for Joint Probability Density Function Modeling of Multiple Wind Farms," Energies, MDPI, vol. 12(7), pages 1-15, April.
    4. Mathieu Langlard & Fabrice Lamadie & Sophie Charton & Johan Debayle, 2021. "Bayesian Inference of a Parametric Random Spheroid from its Orthogonal Projections," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 549-567, June.
    5. 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.
    6. Sreevani, & Murthy, C.A., 2016. "On bandwidth selection using minimal spanning tree for kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 67-84.
    7. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    8. Groß, Marcus & Rendtel, Ulrich & Schmid, Timo & Schmon, Sebastian & Tzavidis, Nikos, 2015. "Estimating the density of ethnic minorities and aged people in Berlin: Multivariate kernel density estimation applied to sensitive geo-referenced administrative data protected via measurement error," Discussion Papers 2015/7, Free University Berlin, School of Business & Economics.
    9. Marcus Groß & Ulrich Rendtel & Timo Schmid & Sebastian Schmon & Nikos Tzavidis, 2017. "Estimating the density of ethnic minorities and aged people in Berlin: multivariate kernel density estimation applied to sensitive georeferenced administrative data protected via measurement error," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 161-183, January.
    10. Perrin, G. & Soize, C. & Ouhbi, N., 2018. "Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 139-154.
    11. Ziane Yasmina & Zougab Nabil & Adjabi Smail, 2021. "Body tail adaptive kernel density estimation for nonnegative heavy-tailed data," Monte Carlo Methods and Applications, De Gruyter, vol. 27(1), pages 57-69, March.
    12. Xijian Hu & Yaori Lu & Huiguo Zhang & Haijun Jiang & Qingdong Shi, 2021. "Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships," Mathematics, MDPI, vol. 9(18), pages 1-14, September.

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