IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v75y2014icp28-38.html
   My bibliography  Save this article

Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314000322
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.02.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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. 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.
    4. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    5. J. Chacón & T. Duong, 2010. "Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 375-398, August.
    6. Horová, Ivana & Koláček, Jan & Vopatová, Kamila, 2013. "Full bandwidth matrix selectors for gradient kernel density estimate," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 364-376.
    7. Kokonendji, Célestin C. & Zocchi, Silvio S., 2010. "Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1655-1662, November.
    8. 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.
    9. Liu, Qing & Pitt, David & Zhang, Xibin & Wu, Xueyuan, 2011. "A Bayesian Approach to Parameter Estimation for Kernel Density Estimation via Transformations," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 181-193, September.
    10. N. Zougab & S. Adjabi & C. Kokonendji, 2012. "Binomial kernel and Bayes local bandwidth in discrete function estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 783-795.
    11. Tarn Duong & Martin L. Hazelton, 2005. "Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506, September.
    12. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
    13. Häggström, Jenny, 2013. "Bandwidth selection for backfitting estimation of semiparametric additive models: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 136-148.
    14. Duong, Tarn, 2007. "ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i07).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    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. 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.
    5. Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.
    6. 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.
    7. Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
    8. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    9. 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.
    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. David Pitt & Montserrat Guillen & Catalina Bolancé, 2011. "Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers XREAP2011-06, Xarxa de Referència en Economia Aplicada (XREAP), revised Jun 2011.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    18. Karim M Abadir & Michel Lubrano, 2023. "Explicit solutions for the asymptotically-optimal bandwidth in cross validation," AMSE Working Papers 2336, Aix-Marseille School of Economics, France.
    19. Horová, Ivana & Koláček, Jan & Vopatová, Kamila, 2013. "Full bandwidth matrix selectors for gradient kernel density estimate," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 364-376.
    20. Schoch, Tobias & Staub, Kaspar & Pfister, Christian, 2012. "Social inequality and the biological standard of living: An anthropometric analysis of Swiss conscription data, 1875–1950," Economics & Human Biology, Elsevier, vol. 10(2), pages 154-173.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:28-38. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.