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Numerical results concerning a sharp adaptive density estimator

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  • Cristina Butucea

    (Humboldt Universität zu Berlin
    Paris 6 University)

Abstract

Summary We present here a simulation study of the behavior of a particular kernel density estimator. It was previously proven that this nonparametric estimator is sharp in the sense of the minimax adaptive theory, which means that it is equally well performing for very smooth or unsmooth densities. The method selects locally both the bandwidth and the kernel function according to the evaluated smoothness of the underlying density. In this paper we describe the method and apply it successfully to i.i.d. simulated data of different probability densities.

Suggested Citation

  • Cristina Butucea, 2001. "Numerical results concerning a sharp adaptive density estimator," Computational Statistics, Springer, vol. 16(2), pages 271-298, July.
    • Handle: RePEc:spr:compst:v:16:y:2001:i:2:d:10.1007_s001800100065
    DOI: 10.1007/s001800100065
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Sheather, Simon J., 1986. "An improved data-based algorithm for choosing the window width when estimating the density at a point," Computational Statistics & Data Analysis, Elsevier, vol. 4(1), pages 61-65, June.
    4. Hall, Peter & Schucany, William R., 1989. "A local cross-validation algorithm," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 109-117, June.
    5. 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.
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