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Universal smoothing factor selection in density estimation: theory and practice

Author

Listed:
  • 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

Abstract

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Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:6:y:1997:i:2:p:223-320
    DOI: 10.1007/BF02564701
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    References listed on IDEAS

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    1. PARK, Byeong U. & TURLACH, Berwin A., 1992. "Practical performance of several data driven bandwidth selectors," LIDAM Reprints CORE 1001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. PARK, Byeong & TURLACH, Berwin, 1992. "Practical performance of several data driven bandwidth selectors," LIDAM Discussion Papers CORE 1992005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. N/A, 1989. "Comments," ILR Review, Cornell University, ILR School, vol. 43(1), pages 89-102, October.
    4. 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.
    5. Jones, M. C., 1991. "The roles of ISE and MISE in density estimation," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 51-56, July.
    6. Daren Cline, 1990. "Optimal kernel estimation of densities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 287-303, June.
    7. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
    8. Devroye, Luc, 1989. "A universal lower bound for the kernel estimate," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 419-423, October.
    9. Yang, L. & Marron, S., 1997. "Iterated Transformation-Kernel Density Estimation," SFB 373 Discussion Papers 1997,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Yang, L., 1996. "Root-n Convergent Transformation-Kernel Density Estimation," SFB 373 Discussion Papers 1996,94, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Park, B. & Turlach, B., 1992. "Practical Performance of Several Data Driven Bandwidih Selectors," Papers 9203, Catholique de Louvain - Institut de statistique.
    12. Marron, J. S., 1989. "Comments on a data based bandwidth selector," Computational Statistics & Data Analysis, Elsevier, vol. 8(2), pages 155-170, July.
    13. Marron, J S, 1988. "Automatic Smoothing Parameter Selection: A Survey," Empirical Economics, Springer, vol. 13(3/4), pages 187-208.
    14. Wand, M. P. & Devroye, Luc, 1993. "How easy is a given density to estimate?," Computational Statistics & Data Analysis, Elsevier, vol. 16(3), pages 311-323, September.
    15. Kim, W. C. & Park, B. U. & Marron, J. S., 1994. "Asymptotically best bandwidth selectors in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 19(2), pages 119-127, January.
    16. Marron, J.S. & Schmitz, H.-P., 1992. "Simultaneous Density Estimation of Several Income Distributions," Econometric Theory, Cambridge University Press, vol. 8(4), pages 476-488, December.
    17. Mammen, Enno, 1990. "A short note on optimal bandwidth selection for kernel estimators," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 23-25, January.
    18. Devroye, Luc, 1994. "On the non-consistency of an estimate of Chiu," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 183-188, June.
    19. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. Luc Devroye & Gábor Lugosi, 1998. "Variable Kernel estimates: On the impossibility of tuning the parameters," Economics Working Papers 325, Department of Economics and Business, Universitat Pompeu Fabra.
    5. 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.
    6. Biau, Gérard & Devroye, Luc, 2005. "Density estimation by the penalized combinatorial method," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 196-208, May.
    7. 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.
    8. 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.
    9. Martínez-Camblor, Pablo & de Uña-Álvarez, Jacobo, 2009. "Non-parametric k-sample tests: Density functions vs distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3344-3357, July.
    10. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2001. "Cluster analysis: a further approach based on density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 441-459, June.
    11. 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.
    12. Pablo Martínez-Camblor & Jacobo Uña-Álvarez, 2013. "Studying the bandwidth in $$k$$ -sample smooth tests," Computational Statistics, Springer, vol. 28(2), pages 875-892, April.

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