IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v34y2019i4d10.1007_s00180-019-00884-0.html
   My bibliography  Save this article

Maximum likelihood method for bandwidth selection in kernel conditional density estimate

Author

Listed:
  • Kateřina Konečná

    (Brno University of Technology, Faculty of Civil Engineering, Institute of Mathematics and Descriptive Geometry
    Masaryk University, Faculty of Science, Department of Mathematics and Statistics)

  • Ivanka Horová

    (Masaryk University, Faculty of Science, Department of Mathematics and Statistics)

Abstract

This paper discusses the kernel estimator of conditional density. A significant problem of kernel smoothing is bandwidth selection. The problem consists in the fact that optimal bandwidth depends on the unknown conditional and marginal density. This is the reason why some data-driven method needs to be applied. In this paper, we suggest a method for bandwidth selection based on a classical maximum likelihood approach. We consider a slight modification of the original method—the maximum likelihood method with one observation being left out. Applied to two types of conditional density estimators—to the Nadaraya–Watson and local linear estimator, the proposed method is compared with other known methods in a simulation study. Our aim is to compare the methods from different points of view, concentrating on the accuracy of the estimated bandwidths, on the final model quality measure, and on the computational time.

Suggested Citation

  • Kateřina Konečná & Ivanka Horová, 2019. "Maximum likelihood method for bandwidth selection in kernel conditional density estimate," Computational Statistics, Springer, vol. 34(4), pages 1871-1887, December.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:4:d:10.1007_s00180-019-00884-0
    DOI: 10.1007/s00180-019-00884-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-019-00884-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-019-00884-0?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. Max Köhler & Anja Schindler & Stefan Sperlich, 2014. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," International Statistical Review, International Statistical Institute, vol. 82(2), pages 243-274, August.
    2. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
    3. B. W. Silverman, 1982. "Kernel Density Estimation Using the Fast Fourier Transform," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(1), pages 93-99, March.
    4. Ivana Horová & Jiří Zelinka, 2007. "Contribution to the bandwidth choice for kernel density estimates," Computational Statistics, Springer, vol. 22(1), pages 31-47, April.
    5. Jan G. De Gooijer & Dawit Zerom, 2003. "On Conditional Density Estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(2), pages 159-176, May.
    6. Chen, Xiaohong & Linton, Oliver & Robinson, Peter, 2001. "The estimation of conditional densities," LSE Research Online Documents on Economics 2312, London School of Economics and Political Science, LSE Library.
    7. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    8. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    9. Bashtannyk, David M. & Hyndman, Rob J., 2001. "Bandwidth selection for kernel conditional density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 279-298, May.
    Full references (including those not matched with items on IDEAS)

    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. Wen, Kuangyu & Wu, Ximing, 2017. "Smoothed kernel conditional density estimation," Economics Letters, Elsevier, vol. 152(C), pages 112-116.
    2. Liang, Han-Ying & Liu, Ai-Ai, 2013. "Kernel estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 40-58.
    3. Otneim, Håkon & Tjøstheim, Dag, 2016. "Non-parametric estimation of conditional densities: A new method," Discussion Papers 2016/22, Norwegian School of Economics, Department of Business and Management Science.
    4. Ann-Kathrin Bott & Michael Kohler, 2016. "Adaptive Estimation of a Conditional Density," International Statistical Review, International Statistical Institute, vol. 84(2), pages 291-316, August.
    5. Wang, Xiao-Feng & Ye, Deping, 2015. "Conditional density estimation in measurement error problems," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 38-50.
    6. Liang, Han-Ying & Peng, Liang, 2010. "Asymptotic normality and Berry-Esseen results for conditional density estimator with censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1043-1054, May.
    7. 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.
    8. Faugeras, Olivier P., 2009. "A quantile-copula approach to conditional density estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2083-2099, October.
    9. repec:ebl:ecbull:v:3:y:2007:i:62:p:1-6 is not listed on IDEAS
    10. Ichimura, Tsuyoshi & Fukuda, Daisuke, 2010. "A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3404-3410, December.
    11. Michael Kohler & Adam Krzyżak, 2020. "Estimating quantiles in imperfect simulation models using conditional density estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 123-155, February.
    12. Han-Ying Liang & Jong-Il Baek, 2016. "Asymptotic normality of conditional density estimation with left-truncated and dependent data," Statistical Papers, Springer, vol. 57(1), pages 1-20, March.
    13. Ann-Kathrin Bott & Michael Kohler, 2017. "Nonparametric estimation of a conditional density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 189-214, February.
    14. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    15. Obbey Elamin & Len Gill & Martyn Andrews, 2020. "Insights from kernel conditional-probability estimates into female labour force participation decision in the UK," Empirical Economics, Springer, vol. 58(6), pages 2981-3006, June.
    16. Jooyoung Jeon & James W. Taylor, 2012. "Using Conditional Kernel Density Estimation for Wind Power Density Forecasting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 66-79, March.
    17. Kim Huynh & David Jacho-Chavez, 2007. "Conditional density estimation: an application to the Ecuadorian manufacturing sector," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-6.
    18. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    19. Chopin, Nicolas & Gadat, Sébastien & Guedj, Benjamin & Guyader, Arnaud & Vernet, Elodie, 2015. "On some recent advances in high dimensional Bayesian Statistics," TSE Working Papers 15-557, Toulouse School of Economics (TSE).
    20. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    21. Xiong, Xianzhu & Ou, Meijuan & Chen, Ailian, 2021. "Reweighted Nadaraya–Watson estimation of conditional density function in the right-censored model," Statistics & Probability Letters, Elsevier, vol. 168(C).

    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:spr:compst:v:34:y:2019:i:4:d:10.1007_s00180-019-00884-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.