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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    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.

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