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A Cross-Validation Bandwidth Choice for Kernel Density Estimates with Selection Biased Data

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  • Wu, Colin O.
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    Abstract

    This paper studies the risks and bandwidth choices of a kernel estimate of the underlying density when the data are obtained fromsindependent biased samples. The main results of this paper give the asymptotic representation of the integrated squared errors and the mean integrated squared errors of the estimate and establish a cross-validation criterion for bandwidth selection. This kernel density estimate is shown to be asymptotically superior to many other intuitive kernel density estimates. The data-driven cross-validation bandwidth is shown to be asymptotically optimal in the sense of Stone (1984,Ann. Statist.12, 1285-1297). The finite sample properties of the cross-validation bandwidth are investigated through a Monte Carlo simulation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 61 (1997)
    Issue (Month): 1 (April)
    Pages: 38-60

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    Handle: RePEc:eee:jmvana:v:61:y:1997:i:1:p:38-60

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    Related research

    Keywords: kernel density estimate integrated squared error bandwidth nonparametric MLE weighted distribution biased sampling model cross-validation;

    References

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    1. Ahmad, Ibrahim A., 1995. "On multivariate kernel estimation for samples from weighted distributions," Statistics & Probability Letters, Elsevier, Elsevier, vol. 22(2), pages 121-129, February.
    2. Marron, James Stephen & Härdle, Wolfgang, 1986. "Random approximations to some measures of accuracy in nonparametric curve estimation," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 20(1), pages 91-113, October.
    3. Colin Wu & Andrew Mao, 1996. "Minimax kernels for density estimation with biased data," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 48(3), pages 451-467, September.
    4. Morgenthaler, S. & Vardi, Y., 1986. "Choice-based samples : A non-parametric approach," Journal of Econometrics, Elsevier, Elsevier, vol. 32(1), pages 109-125, June.
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    Cited by:
    1. José Cristóbal & José Alcalá, 2001. "An overview of nonparametric contributions to the problem of functional estimation from biased data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 10(2), pages 309-332, December.

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