IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v22y2010i1p105-114.html
   My bibliography  Save this article

Improving Sheather and Jones’ bandwidth selector for difficult densities in kernel density estimation

Author

Listed:
  • J. Liao
  • Yujun Wu
  • Yong Lin

Abstract

Kernel density estimation is a widely used statistical tool and bandwidth selection is critically important. The Sheather and Jones’ (SJ) selector [A reliable data-based bandwidth selection method for kernel density estimation, J. R. Stat. Soc. Ser. B 53 (1991), pp. 683–690] remains the best available data-driven bandwidth selector. It can, however, perform poorly if the true density deviates too much in shape from normal. This paper first develops an alternative selector by following ideas in Park and Marron [On the use of pilot estimators in bandwidth selection, Nonparametr. Stat. 1 (1992), pp. 231–240] to reduce the impact of the normal reference density. The selector can bring drastic improvement to less smooth densities that the SJ selector has difficulty with, but may be slightly worse off otherwise. We then propose to combine the alternative selector and SJ selector by using the smaller of the two bandwidths, which has the effect of automatically picking the better one for a particular density. In our extensive simulation, study using the 15 benchmark densities in Marron and Wand [Exact mean integrated squared error, Ann. Statist. 20 (1992), pp. 712–736], the combined selector significantly improves the SJ selector for 5 difficult densities and retains the superior performance of the SJ selector for the other 10. A ready-to-use R function is provided.

Suggested Citation

  • J. Liao & Yujun Wu & Yong Lin, 2010. "Improving Sheather and Jones’ bandwidth selector for difficult densities in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 105-114.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:105-114
    DOI: 10.1080/10485250903194003
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250903194003
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485250903194003?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. Duc Devroye & J. Beirlant & R. Cao & R. Fraiman & P. Hall & M. Jones & Gábor Lugosi & E. Mammen & J. Marron & C. Sánchez-Sellero & J. Uña & F. Udina & L. Devroye, 1997. "Universal smoothing factor selection in density estimation: theory and practice," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 223-320, December.
    2. Jones, M. C. & Sheather, S. J., 1991. "Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 511-514, June.
    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. Christophe Corbier, 2016. "Huberian function applied to neurodegenerative disorder gait rhythm," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2065-2084, August.
    2. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    3. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.
    4. 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.

    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. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    2. Miguel Reyes & Mario Francisco-Fernández & Ricardo Cao, 2017. "Bandwidth selection in kernel density estimation for interval-grouped data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 527-545, September.
    3. José E. Chacón & Carlos Tenreiro, 2012. "Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 523-548, September.
    4. Mokkadem, Abdelkader & Pelletier, Mariane, 2020. "Online estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 166(C).
    5. Hall, Peter & Wolff, Rodney C. L., 1995. "Estimators of integrals of powers of density derivatives," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 105-110, August.
    6. Rudolf Grübel, 1994. "Estimation of density functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 67-75, March.
    7. T. Sclocco & M. Marzio, 2001. "A note on kernel density estimation for non-negative random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 67-79, January.
    8. Langrené, Nicolas & Warin, Xavier, 2021. "Fast multivariate empirical cumulative distribution function with connection to kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    9. Moreira, C. & Van Keilegom, I., 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 107-123.
    10. Christopher Withers & Saralees Nadarajah, 2011. "Nonparametric confidence intervals for the integral of a function of an unknown density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 943-966.
    11. Sidibé, I.B. & Khatab, A. & Diallo, C. & Adjallah, K.H., 2016. "Kernel estimator of maintenance optimization model for a stochastically degrading system under different operating environments," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 109-116.
    12. Luc Devroye & Gábor Lugosi & Frederic Udina, 1998. "Inequalities for a new data-based method for selecting nonparametric density estimates," Economics Working Papers 281, Department of Economics and Business, Universitat Pompeu Fabra.
    13. Gonzalez-Manteiga, W. & Sanchez-Sellero, C. & Wand, M. P., 1996. "Accuracy of binned kernel functional approximations," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 1-16, June.
    14. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
    15. Wang, Qing & Lindsay, Bruce G., 2015. "Improving cross-validated bandwidth selection using subsampling-extrapolation techniques," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 51-71.
    16. Suojin Wang, 1995. "Optimizing the smoothed bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 65-80, January.
    17. Saavedra, Ángeles & Cao, Ricardo, 1999. "Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 129-155, April.
    18. 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.
    19. 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.
    20. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.

    More about this item

    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:taf:gnstxx:v:22:y:2010:i:1:p:105-114. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.