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Kernel estimation for a superpopulation probability density function under informative selection

Author

Listed:
  • Daniel Bonnéry

    (University of Maryland)

  • F. Jay Breidt

    (Colorado State University)

  • François Coquet

    (Irmar and Ensai)

Abstract

Kernel density estimation of the probability density function (pdf) of a response variable is considered under informative selection from a finite population. The informative selection implies that the conditional pdf of a response, given that it was selected for observation, is not the same as the inferential target, which is the unconditional pdf of the response in the superpopulation. Instead, the pdf of the observations (sample pdf) is a weighted version of the superpopulation pdf of interest. Properties of the standard kernel density estimator are described under an asymptotic framework that covers a wide range of informative selection mechanisms. The theory allows for the possibility that the selection mechanism has a parametric structure. A variety of adjustments (parametric or nonparametric) to account for the informative selection are proposed, and investigated via simulation.

Suggested Citation

  • Daniel Bonnéry & F. Jay Breidt & François Coquet, 2017. "Kernel estimation for a superpopulation probability density function under informative selection," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 301-318, December.
    • Handle: RePEc:spr:metron:v:75:y:2017:i:3:d:10.1007_s40300-017-0127-x
    DOI: 10.1007/s40300-017-0127-x
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    References listed on IDEAS

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    1. Jean-François Beaumont, 2008. "A new approach to weighting and inference in sample surveys," Biometrika, Biometrika Trust, vol. 95(3), pages 539-553.
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    Cited by:

    1. Sayed A. Mostafa & Ibrahim A. Ahmad, 2019. "Kernel density estimation from complex surveys in the presence of complete auxiliary information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(3), pages 295-338, April.
    2. Jean D. Opsomer & M. Giovanna Ranalli & Maria Michela Dickson, 2017. "Foreword to the special issue on “Advances in Survey Statistics”," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 245-247, December.
    3. Sayed A. Mostafa & Ibrahim A. Ahmad, 2021. "Kernel Density Estimation Based on the Distinct Units in Sampling with Replacement," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 507-547, November.

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