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Kernel density estimation from complex surveys in the presence of complete auxiliary information

Author

Listed:
  • Sayed A. Mostafa

    (Indiana University
    North Carolina A&T State University)

  • Ibrahim A. Ahmad

    (Oklahoma State University)

Abstract

Auxiliary information is widely used in survey sampling to enhance the precision of estimators of finite population parameters, such as the finite population mean, percentiles, and distribution function. In the context of complex surveys, we show how auxiliary information can be used effectively in kernel estimation of the superpopulation density function of a given study variable. We propose two classes of “model-assisted” kernel density estimators that make efficient use of auxiliary information. For one class we assume that the functional relationship between the study variable Y and the auxiliary variable X is known, while for the other class the relationship is assumed unknown and is estimated using kernel smoothing techniques. Under the first class, we show that if the functional relationship can be written as a simple linear regression model with constant error variance, the mean of the proposed density estimator will be identical to the well-known regression estimator of the finite population mean. If we drop the intercept from the linear model and allow the error variance to be proportional to the auxiliary variable, the mean of the proposed density estimator matches the ratio estimator of the finite population mean. The properties of the new density estimators are studied under a combined design-model-based inference framework, which accounts for the underlying superpopulation model as well as the randomization distribution induced by the sampling design. Moreover, the asymptotic normality of each estimator is derived under both design-based and combined inference frameworks when the sampling design is simple random sampling without replacement. For the practical implementation of these estimators, we discuss how data-driven bandwidth estimators can be obtained. The finite sample properties of the proposed estimators are addressed via simulations and an example that mimics a real survey. These simulations show that the new estimators perform very well compared to standard kernel estimators which do not utilize the auxiliary information.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:3:d:10.1007_s00184-018-0703-y
    DOI: 10.1007/s00184-018-0703-y
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    References listed on IDEAS

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    1. Breunig, Robert, 2008. "Nonparametric density estimation for stratified samples," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2194-2200, October.
    2. Robert Breunig, 2001. "Density Estimation For Clustered Data," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 353-367.
    3. Yao, Qiwei & Tong, Howell, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics 19426, London School of Economics and Political Science, LSE Library.
    4. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    5. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    6. Torsten Harms & Pierre Duchesne, 2010. "On kernel nonparametric regression designed for complex survey data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 111-138, July.
    7. Ingrid K. Glad & Nils Lid Hjort & Nikolai G. Ushakov, 2003. "Correction of Density Estimators that are not Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 415-427, June.
    8. F. J. Breidt & G. Claeskens & J. D. Opsomer, 2005. "Model-assisted estimation for complex surveys using penalised splines," Biometrika, Biometrika Trust, vol. 92(4), pages 831-846, December.
    9. Scott, David W., 2004. "Multivariate Density Estimation and Visualization," Papers 2004,16, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    10. 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.
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    Cited by:

    1. 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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