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Practical performance of several data driven bandwidth selectors


  • PARK, Byeong
  • TURLACH, Berwin

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)


Most recently proposed bandwidth selectors in kernel density estimation have been developed with intent to reduce the large sampling variability of Least Squares Cross-Validation. Their asymptotic superiority has been shown in many papers. Some of those selectors have even the fastest n-1/ 2 relative rate of convergence to their theoretical optimum. The aim of this paper is to see what is happening for small sample sizes. Several recently proposed methods of bandwidth selection are considered. These methods are compared to Least Squares Cross-Validation through simulations. Some qualitative measures of performance as well as quantitative ones are used for this comparison. It is seen that, while most of the bandwidth selectors gain some in terms of variance reduction, some of them lose a lot in terms of increased bias resulting in inferior overall performance when compared to Least Squares Cross-Validation.

Suggested Citation

  • PARK, Byeong & TURLACH, Berwin, 1992. "Practical performance of several data driven bandwidth selectors," CORE Discussion Papers 1992005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1992005

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    5. M. M. Salinas-Jimenez, 2003. "Technological change, efficiency gains and capital accumulation in labour productivity growth and convergence: an application to the Spanish regions," Applied Economics, Taylor & Francis Journals, vol. 35(17), pages 1839-1851.
    6. Emili Tortosa-Ausina, 2000. "Inefficient banks or inefficient assets," Working Papers 0005, Departament Empresa, Universitat Autònoma de Barcelona, revised Dec 2000.
    7. Berwin A. TURLACH, "undated". "Bandwidth selection in kernel density estimation: a rewiew," Statistic und Oekonometrie 9307, Humboldt Universitaet Berlin.
    8. Cwik, J. & Koronacki, J., 1997. "A combined adaptive-mixtures/plug-in estimator of multivariate probability densities," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 199-218, December.
    9. Wolfgang HAERDLE & Marlene MUELLER, "undated". "Nichtparametrische Glaettungsmethoden in der alltaeglichen statistischen Praxis," Statistic und Oekonometrie 9208, Humboldt Universitaet Berlin.
    10. Emili Tortosa-Ausina, 2003. "Bank cost efficiency as distribution dynamics: controlling for specialization is important," Investigaciones Economicas, Fundación SEPI, vol. 27(1), pages 71-96, January.
    11. Seok-Oh Jeong & Byeong Park & Léopold Simar, 2010. "Nonparametric conditional efficiency measures: asymptotic properties," Annals of Operations Research, Springer, vol. 173(1), pages 105-122, January.
    12. 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.
    13. R. Carter Hill & Kang-sun Lee, 2001. "Performance of Bandwidth Selection Rules for the Local Linear Regression," Departmental Working Papers 2001-10, Department of Economics, Louisiana State University.
    14. Kang, Sung Jin & Lee, Myoungjae, 2005. "Q-convergence with interquartile ranges," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1785-1806, October.
    15. Farmen, Mark & Marron, J. S., 1999. "An assessment of finite sample performance of adaptive methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 143-168, April.
    16. Curran, Declan & Funke, Michael & Wang, Jue, 2007. "Economic growth across space and time : subprovincial evidence from mainland China," BOFIT Discussion Papers 21/2007, Bank of Finland, Institute for Economies in Transition.
    17. Subrata Kundu & Adam Martinsek, 1997. "Bounding the L1 Distance in Nonparametric Density Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 57-78, March.
    18. Lauzon, Darren & Corak, Miles, 2005. "Differences entre les distributions du rendement scolaire au secondaire : le role de la taille de la classe et du temps d'enseignement," Direction des études analytiques : documents de recherche 2005270f, Statistics Canada, Direction des études analytiques.
    19. Giordano, F. & Parrella, M.L., 2008. "Neural networks for bandwidth selection in local linear regression of time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2435-2450, January.
    20. Tortosa-Ausina, Emili, 2002. "Exploring efficiency differences over time in the Spanish banking industry," European Journal of Operational Research, Elsevier, vol. 139(3), pages 643-664, June.
    21. Jos'e E. Figueroa-L'opez & Cheng Li, 2016. "Optimal Kernel Estimation of Spot Volatility of Stochastic Differential Equations," Papers 1612.04507,
    22. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Robust Kernel Estimator For Densities Of Unknown," Departmental Working Papers 2005-05, McGill University, Department of Economics.
    23. Docquier, Frédéric & Lohest, Olivier & Marfouk, Abdeslam, 2005. "Brain Drain in Developing Regions (1990-2000)," IZA Discussion Papers 1668, Institute of Labor Economics (IZA).
    24. Emili Tortosa Ausina, 1999. "-Convergence In Efficiency Of The Spanish Banking Firms As Distribution Dynamics," Working Papers. Serie EC 1999-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    25. Marco BIANCHI, "undated". "A simple and fast method of regime shifts detection based on kernel density estimation," Statistic und Oekonometrie 9316, Humboldt Universitaet Berlin.

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