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Bandwidth selection for kernel density estimation with length-biased data

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  • M. I. Borrajo
  • W. González-Manteiga
  • M. D. Martínez-Miranda

Abstract

Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the context of length-biased data, proposing two consistent bootstrap methods that we use for bandwidth selection. Apart from the bootstrap bandwidth selectors we suggest a rule-of-thumb. These bandwidth selection proposals are compared with a least-squares cross-validation method. A simulation study is accomplished to understand the behaviour of the procedures in finite samples.

Suggested Citation

  • M. I. Borrajo & W. González-Manteiga & M. D. Martínez-Miranda, 2017. "Bandwidth selection for kernel density estimation with length-biased data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 636-668, July.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:636-668
    DOI: 10.1080/10485252.2017.1339309
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    Cited by:

    1. Arup Bose & Santanu Dutta, 2022. "Kernel based estimation of the distribution function for length biased data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 269-287, April.
    2. Rajesh, Richu & G., Rajesh & Sunoj, S.M., 2022. "Kernel estimation of extropy function under length-biased sampling," Statistics & Probability Letters, Elsevier, vol. 181(C).
    3. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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