IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i3p732-740.html
   My bibliography  Save this article

Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions

Author

Listed:
  • Hu, Shuowen
  • Poskitt, D.S.
  • Zhang, Xibin

Abstract

In this paper, we propose a new methodology for multivariate kernel density estimation in which data are categorized into low- and high-density regions as an underlying mechanism for assigning adaptive bandwidths. We derive the posterior density of the bandwidth parameters via the Kullback–Leibler divergence criterion and use a Markov chain Monte Carlo (MCMC) sampling algorithm to estimate the adaptive bandwidths. The resulting estimator is referred to as the tail-adaptive density estimator. Monte Carlo simulation results show that the tail-adaptive density estimator outperforms the global-bandwidth density estimators implemented using different global bandwidth selection rules. The inferential potential of the tail-adaptive density estimator is demonstrated by employing the estimator to estimate the bivariate density of daily index returns observed from the USA and Australian stock markets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:732-740
    DOI: 10.1016/j.csda.2011.09.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003537
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.09.022?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stephan R. Sain & David W. Scott, 2002. "Zero‐Bias Locally Adaptive Density Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 441-460, September.
    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. Abramson, Ian S., 1982. "Arbitrariness of the pilot estimator in adaptive kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 562-567, December.
    4. 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.
    5. 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.
    6. Marron, J. S. & Nolan, D., 1988. "Canonical kernels for density estimation," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 195-199, December.
    7. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    8. M. Jácome & I. Gijbels & R. Cao, 2008. "Comparison of presmoothing methods in kernel density estimation under censoring," Computational Statistics, Springer, vol. 23(3), pages 381-406, July.
    9. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    10. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. 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.
    13. Holmes, Michael P. & Gray, Alexander G. & Isbell Jr., Charles Lee, 2010. "Fast kernel conditional density estimation: A dual-tree Monte Carlo approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1707-1718, July.
    14. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
    15. Philippe Vieu, 1999. "Multiple Kernel Procedure: an Asymptotic Support," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 61-72, March.
    16. Horová Ivana & Vieu Philippe & Zelinka Jiří, 2002. "Optimal Choice Of Nonparametric Estimates Of A Density And Of Its Derivatives," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 355-378, April.
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    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. 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.
    2. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2021. "Bayesian estimation for a semiparametric nonlinear volatility model," Economic Modelling, Elsevier, vol. 98(C), pages 361-370.
    3. 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.
    4. 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.
    5. Iseringhausen, Martin, 2024. "A time-varying skewness model for Growth-at-Risk," International Journal of Forecasting, Elsevier, vol. 40(1), pages 229-246.
    6. 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.
    7. 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.
    8. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    9. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    10. Tobias Adrian & Nina Boyarchenko & Domenico Giannone, 2019. "Vulnerable Growth," American Economic Review, American Economic Association, vol. 109(4), pages 1263-1289, April.
    11. 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.
    12. Adams, Patrick A. & Adrian, Tobias & Boyarchenko, Nina & Giannone, Domenico, 2021. "Forecasting macroeconomic risks," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1173-1191.
    13. 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.
    14. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    15. Shukur, Ghazi & Zeebari, Zangin, 2011. "On the median regression for SURE models with applications to 3-generation immigrants data in Sweden," Economic Modelling, Elsevier, vol. 28(6), pages 2566-2578.
    16. Levent C. Uslu & Burak Evre, 2017. "Liquidity Adjusted Value At Risk: Integrating The Uncertainty In Depth And Tightness," Eurasian Journal of Business and Management, Eurasian Publications, vol. 5(1), pages 55-69.
    17. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    18. Anastasios Panagiotelis & Michael S. Smith & Peter J. Danaher, 2014. "From Amazon to Apple: Modeling Online Retail Sales, Purchase Incidence, and Visit Behavior," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 14-29, January.
    19. Xibin Zhang & Maxwell L. King & Rob J. Hyndman, 2004. "Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC," Monash Econometrics and Business Statistics Working Papers 9/04, Monash University, Department of Econometrics and Business Statistics.
    20. 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.

    More about this item

    Keywords

    Marginal likelihood; Markov chain Monte Carlo; S&P 500 index; Value-at-risk;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    Statistics

    Access and download statistics

    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:56:y:2012:i:3:p:732-740. 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.