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Exploring the use of variable bandwidth kernel density estimators


  • Isaias H. Salgado-Ugarte

    () (F.E.S. Zaragoza U.N.A.M. Biologia)

  • Marco A. Perez-Hernandez

    () (Depto. de Biologia, U.A.M. Iztapalapa, Mexico)


Variable bandwidth kernel density estimators increase the window width at low densities and decrease it where data concentrate. This represents an improvement over the fixed bandwidth kernel density estimators. In this article, we explore the use of one implementation of a variable kernel estimator in conjunction with several rules and procedures for bandwidth selection applied to several real datasets. The considered examples permit us to state that when working with tens or a few hundreds of data observations, least-squares cross-validation bandwidth rarely produces useful estimates; with thousands of observations, this problem can be surpassed. Optimal bandwidth and biased cross-validation (BCV), in general, oversmooth multimodal densities. The Sheather-Jones plug-in rule produced bandwidths that behave slightly better in this respect. The Silverman test is considered as a very sophisticated and safe procedure to estimate the number of modes in univariate distributions; however, similar results could be obtained with the Sheather-Jones rule, but at a much lower computational cost. As expected, the variable bandwidth kernel density estimates showed fewer modes than those chosen by the Silverman test, especially those distributions in which multimodality was caused by several noisy minor modes. More research on the subject is needed. Copyright 2003 by Stata Corporation.

Suggested Citation

  • Isaias H. Salgado-Ugarte & Marco A. Perez-Hernandez, 2003. "Exploring the use of variable bandwidth kernel density estimators," Stata Journal, StataCorp LP, vol. 3(2), pages 133-147, June.
  • Handle: RePEc:tsj:stataj:v:3:y:2003:i:2:p:133-147

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    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Vivek Dehejia & Marcel Voia, 2008. "International Income Comparisons and Location Choice: Methodology, Analysis, and Implications," Carleton Economic Papers 08-02, Carleton University, Department of Economics.
    2. Céline Bonnefond & Matthieu Clément, 2012. "An analysis of income polarisation in rural and urban China," Post-Communist Economies, Taylor & Francis Journals, vol. 24(1), pages 15-37, June.
    3. Chong Terence Tai-Leung & Poon Ka-Ho, 2017. "A new recognition algorithm for “head-and-shoulders” price patterns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-18, December.
    4. Philippe Van Kerm, 2003. "Adaptive kernel density estimation," Stata Journal, StataCorp LP, vol. 3(2), pages 148-156, June.


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