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A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator

Author

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  • Max de Lima
  • Gregorio Atuncar

Abstract

The estimation of multivariate densities using the kernel method has wide applicability. However, this problem has received less attention than the univariate case. This is mainly due to the increasing difficulty in estimating the optimal smoothing matrix, especially when the components are correlated. To overcome this difficulty, we propose in this work a Bayesian method to estimate the optimal smoothing matrix H. A loss function is defined and the estimator of H is the matrix minimising the loss function. We carried out simulations with a mixture of multivariate densities with correlation and the results were highly satisfactory.

Suggested Citation

  • Max de Lima & Gregorio Atuncar, 2011. "A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 137-148.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:137-148
    DOI: 10.1080/10485252.2010.485200
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    Citations

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    Cited by:

    1. Y. Ziane & S. Adjabi & N. Zougab, 2015. "Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1645-1658, August.
    2. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
    3. 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.
    4. Tingting Cheng & Jiti Gao & Xibin Zhang, 2014. "Semiparametric Localized Bandwidth Selection in Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 14/14, Monash University, Department of Econometrics and Business Statistics.
    5. Pianpool Kamoljitprapa & Fazil M. Baksh & Andrea De Gaetano & Orathai Polsen & Piyachat Leelasilapasart, 2023. "Statistical Study Design for Analyzing Multiple Gene Loci Correlation in DNA Sequences," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
    6. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.
    7. Tingting Cheng & Jiti Gao & Xibin Zhang, 2019. "Nonparametric localized bandwidth selection for Kernel density estimation," Econometric Reviews, Taylor & Francis Journals, vol. 38(7), pages 733-762, August.
    8. Zhang, Xibin & King, Maxwell L. & Shang, Han Lin, 2014. "A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 218-234.
    9. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2011. "Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 10/11, Monash University, Department of Econometrics and Business Statistics.
    10. Guohua Feng & Chuan Wang & Xibin Zhang, 2019. "Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach," Journal of Productivity Analysis, Springer, vol. 51(1), pages 1-19, February.
    11. Filippone, Maurizio & Sanguinetti, Guido, 2011. "Approximate inference of the bandwidth in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3104-3122, December.
    12. Tingting Cheng & Jiti Gao & Xibin Zhang, 2014. "Semiparametric Localized Bandwidth Selection for Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 27/14, Monash University, Department of Econometrics and Business Statistics.

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