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Sample distribution function based goodness-of-fit test for complex surveys

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  • Wang, Jianqiang C.

Abstract

Testing the parametric distribution of a random variable is a fundamental problem in exploratory and inferential statistics. Classical empirical distribution function based goodness-of-fit tests typically require the data to be an independent and identically distributed realization of a certain probability model, and thus would fail when complex sampling designs introduce dependency and selection bias to the realized sample. In this paper, we propose goodness-of-fit procedures for a survey variable. To this end, we introduce several divergence measures between the design weighted estimator of distribution function and the hypothesized distribution, and propose goodness-of-fit tests based on these divergence measures. The test procedures are substantiated by theoretical results on the convergence of the estimated distribution function to the superpopulation distribution function on a metric space. We also provide computational details on how to calculate test p-values, and demonstrate the performance of the proposed test through simulation experiments. Finally, we illustrate the utility of the proposed test through the analysis of US 2004 presidential election data.

Suggested Citation

  • Wang, Jianqiang C., 2012. "Sample distribution function based goodness-of-fit test for complex surveys," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 664-679.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:664-679
    DOI: 10.1016/j.csda.2011.09.015
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    References listed on IDEAS

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    1. Hervé Cardot & Etienne Josserand, 2011. "Horvitz--Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling," Biometrika, Biometrika Trust, vol. 98(1), pages 107-118.
    2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, November.
    3. Lumley, Thomas, 2004. "Analysis of Complex Survey Samples," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i08).
    4. C. Goga & J.-C. Deville & A. Ruiz-Gazen, 2009. "Use of functionals in linearization and composite estimation with application to two-sample survey data," Biometrika, Biometrika Trust, vol. 96(3), pages 691-709.
    5. Jiang, Jiming & Lahiri, P., 2006. "Estimation of Finite Population Domain Means: A Model-Assisted Empirical Best Prediction Approach," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 301-311, March.
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    Cited by:

    1. Patrice Bertail & Emilie Chautru & Stephan Clémençon, 2017. "Empirical Processes in Survey Sampling with (Conditional) Poisson Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 97-111, March.
    2. M. D. Jiménez-Gamero & J. L. Moreno-Rebollo & J. A. Mayor-Gallego, 2018. "On the estimation of the characteristic function in finite populations with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 95-121, March.

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