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Bayesian Empirical Likelihood Methods

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Sampling Theory and Practice

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

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Abstract

In this chapter, we first provide a brief review of Bayesian approaches to finite population inference. We then present Bayesian empirical likelihood methods for the finite population mean as well as general parameters defined through estimating functions. The focus is on how to formulate the inferential procedures under the Bayesian framework, and discussions of design-based frequentist properties of Bayesian point estimators and credible intervals.

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References

  • Aitkin, M. (2008). Applications of the Bayesian bootstrap in finite population inference. Journal of Official Statistics, 24, 21–51.

    Google Scholar 

  • Ericson, W. A. (1969). Subjective Bayesian models in sampling finite populations, I. Journal of the Royal Statistical Society, Series B, 31, 195–234.

    MathSciNet  MATH  Google Scholar 

  • Godambe, V. P. (1966). A new approach to sampling from finite populations. Journal of the Royal Statistical Society, Series B, 28, 310–328.

    MATH  Google Scholar 

  • Godambe, V. P. (1968). Bayesian sufficiency in survey-sampling. Annals of Mathematical Statistics, 20, 363–373.

    Article  MathSciNet  Google Scholar 

  • Godambe, V. P., & Thompson, M. E. (1971). Bayes, fiducial and frequency aspects of statistical inference in regression analysis in survey-sampling. Journal of the Royal Statistical Society, Series B, 33, 361–390.

    MathSciNet  MATH  Google Scholar 

  • Hansen, M. H., Madow, W. G., & Tepping, B. J. (1983). An evaluation of model-dependent and probability-sampling inferences in sample surveys. Journal of the American Statistical Association, 78, 776–793.

    Article  Google Scholar 

  • Hartley, H. O., & Rao, J. N. K. (1968). A new estimation theory for sample surveys. Biometrika, 55, 547–557.

    Article  Google Scholar 

  • Hoadley, B. (1969). The compound multinomial distribution and Bayesian analysis of categorical data from finite populations. Journal of the American Statistical Association, 64, 216–229.

    Article  MathSciNet  Google Scholar 

  • Lazar, N. A. (2003). Bayesian empirical likelihood. Biometrika, 90, 319–326.

    Article  MathSciNet  Google Scholar 

  • Little, R. J. A. (2011). Calibrated Bayes, for statistics in general, and missing data in particular. Statistical Science, 26, 162–174.

    Article  MathSciNet  Google Scholar 

  • Meeden, G., & Vardeman, S. (1991) A non-informative Bayesian approach to interval estimation in finite population sampling. Journal of the American Statistical Association, 86, 972–980.

    Article  MathSciNet  Google Scholar 

  • Narisetty, N. N., & He, X. (2014). Bayesian variable selection with shrinking and diffusing priors. Annals of Statistics, 42, 789–817.

    Article  MathSciNet  Google Scholar 

  • Neyman, J. (1934). On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. Journal of the Royal Statistical Society, 97, 558–606.

    Article  Google Scholar 

  • Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75, 237–249.

    Article  MathSciNet  Google Scholar 

  • Rao, J. N. K. (2011). Impact of frequentist and Bayesian methods on survey sampling practice: A selective appraisal. Statistical Science, 26, 240–256.

    Article  MathSciNet  Google Scholar 

  • Rao, J. N. K., & Ghangurde, P. D. (1972). Bayesian optimization in sampling finite populations. Journal of the American Statistical Association, 67, 439–443.

    Article  MathSciNet  Google Scholar 

  • Rao, J. N. K., & Molina, I. (2015). Small area estimation (2nd ed.). Hoboken, NJ: Wiley.

    Book  Google Scholar 

  • Rao, J. N. K., & Wu, C. (2009). Empirical likelihood methods. In D. Pfeffermann & C. R. Rao (Eds.), Handbook of Statistics, Vol. 29B: Sample Surveys: Inference and Analysis (pp. 189–207). Amsterdam: Elsevier.

    Google Scholar 

  • Rao, J. N. K., & Wu, C. (2010a). Bayesian pseudo empirical likelihood intervals for complex surveys. Journal of the Royal Statistical Society, Series B, 72, 533–544.

    Article  MathSciNet  Google Scholar 

  • Royall, R. M. (1970). On finite population sampling theory under certain linear regression models. Biometrika, 57, 377–387.

    Article  Google Scholar 

  • Royall, R. M., & Pfeffermann, D. (1982). Balanced samples and robust Bayesian inference in finite population sampling. Biometrika, 69, 401–409.

    Article  MathSciNet  Google Scholar 

  • Wasserman, L. (2000). Asymptotic inference for mixture models using data-dependent priors. Journal of the Royal Statistical Society, Series B, 62, 159–180.

    Article  MathSciNet  Google Scholar 

  • Yang, Y., & He, X. (2012). Bayesian empirical likelihood for quantile regression. The Annals of Statistics, 40, 1102–1131.

    Article  MathSciNet  Google Scholar 

  • Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g prior distributions. In P. Goel & A. Zellner (Eds.), Bayesian Inference and Decision Techniques (pp. 233–243). New York: Elsevier.

    Google Scholar 

  • Zellner, A., & Siow, A. (1980). Posterior odds ratios for selected regression hypotheses. In J. M. Bernardo, M. H. DeGroot, D. V. Lindley, & A. F. M. Smith (Eds.), Bayesian Statistics: Proceedings of the First International Meeting Held in Valencia (pp. 585–603). Valencia: University of Valencia Press.

    Google Scholar 

  • Zhao, P., Ghosh, M., Rao, J. N. K., & Wu, C. (2020a). Bayesian empirical likelihood inference with complex survey data. Journal of the Royal Statistical Society, Series B, 82, 155–174.

    Article  Google Scholar 

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Wu, C., Thompson, M.E. (2020). Bayesian Empirical Likelihood Methods. In: Sampling Theory and Practice. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-44246-0_11

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