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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

This chapter presents empirical likelihood methods for complex surveys. We first focus on point estimation and confidence intervals for the single descriptive finite population mean using the pseudo empirical likelihood method. We then develop general inferential procedures for parameters defined through estimating equations using either the pseudo empirical likelihood approach or the sample empirical likelihood approach. When the population size is unknown and the parameter of interest is the population total, a generalized pseudo empirical likelihood method can be used.

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References

  • Berger, Y. G. (1998). Rate of convergence to normal distribution for the Horvitz-Thompson estimator. Journal of Statistical Planning and Inference, 67, 209–226.

    Article  MathSciNet  Google Scholar 

  • Berger, Y. G., & De La Riva Torres, O. (2016). Empirical likelihood confidence intervals for complex sampling designs. Journal of the Royal Statistical Society, Series B, 78, 319–341.

    Article  MathSciNet  Google Scholar 

  • Chen, J., Chen, S. Y., & Rao, J. N. K. (2003). Empirical likelihood confidence intervals for the mean of a population containing many zero values. The Canadian Journal of Statistics, 31, 53–68.

    Article  MathSciNet  Google Scholar 

  • Chen, J., & Qin, J. (1993). Empirical likelihood estimation for finite populations and the effective usage of auxiliary information. Biometrika, 80, 107–116.

    Article  MathSciNet  Google Scholar 

  • Chen, J., & Sitter, R. R. (1999). A pseudo empirical likelihood approach to the effective use of auxiliary information in complex surveys. Statistica Sinica, 9, 385–406.

    MathSciNet  MATH  Google Scholar 

  • Chen, J., Sitter, R. R., & Wu, C. (2002). Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys. Biometrika, 89, 230–237.

    Article  MathSciNet  Google Scholar 

  • Chen, S., & Kim, J. K. (2014). Population empirical likelihood for nonparametric inference in survey sampling. Statistica Sinica, 24, 335–355.

    MathSciNet  MATH  Google Scholar 

  • Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96, 1348–60.

    Article  MathSciNet  Google Scholar 

  • Fu, Y., Wang, X., & Wu, C. (2009). Weighted empirical likelihood inference for multiple samples. Journal of Statistical Planning and Inference, 139, 1462–1473.

    Article  MathSciNet  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 

  • Hájek, J. (1964). Asymptotic theory of rejective sampling with varying probabilities from a finite population. Annals of Mathematical Statistics, 35, 1491–1523.

    Article  MathSciNet  Google Scholar 

  • Hájek, J. (1981). Sampling from a finite population. New York: Marcel Dekker.

    MATH  Google Scholar 

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

    Article  Google Scholar 

  • Hartley, H. O., & Rao, J. N. K. (1969). A new estimation theory for sample surveys, II. In N. L. Johnson & H. Smith (Eds.), New developments in survey sampling (pp. 147–169). New York: Wiley.

    Google Scholar 

  • Leng, C., & Tang, C. Y. (2012). Penalized empirical likelihood and growing dimensional general estimating equations. Biometrika, 99, 703–716.

    Article  MathSciNet  Google Scholar 

  • Oguz-Alper, M., & Berger, Y. G. (2016). Modelling complex survey data with population level Information: An empirical likelihood approach. Biometrika, 103, 447–459.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Owen, A. B. (2001). Empirical likelihood. New York: Chapman & Hall/CRC.

    Book  Google Scholar 

  • Qin, J., & Lawless, J. F. (1994). Empirical likelihood and general estimating equations. Annals of Statistics, 22, 300–325.

    Article  MathSciNet  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 

  • Tan, Z. (2013). Simple design-efficient calibration estimators for rejective and high-entropy sampling. Biometrika, 100, 399–415.

    Article  MathSciNet  Google Scholar 

  • Tan, Z., & Wu, C. (2015). Generalized pseudo empirical likelihood inferences for complex surveys. The Canadian Journal of Statistics, 43, 1–17.

    Article  MathSciNet  Google Scholar 

  • Tang, C. Y., & Leng, C. (2010). Penalized high dimensional empirical likelihood. Biometrika, 97, 905–920.

    Article  MathSciNet  Google Scholar 

  • Tibshirani, R. J. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society, Series B, 58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Wu, C. (2004a). Some algorithmic aspects of the empirical likelihood method in survey sampling. Statistica Sinica, 14, 1057–1067.

    MathSciNet  MATH  Google Scholar 

  • Wu, C. (2005). Algorithms and R codes for the pseudo empirical likelihood method in survey sampling. Survey Methodology, 31, 239–243.

    Google Scholar 

  • Wu, C., & Rao, J. N. K. (2006). Pseudo empirical likelihood ratio confidence intervals for complex surveys. The Canadian Journal of Statistics, 34, 359–375.

    Article  MathSciNet  Google Scholar 

  • Wu, C., & Rao, J. N. K. (2010). Bootstrap procedures for the pseudo empirical likelihood method in sample surveys. Statistics and Probability Letters, 80, 1472–1478.

    Article  MathSciNet  Google Scholar 

  • Wu, C., & Yan, Y. (2012). Weighted empirical likelihood inference for two-sample problems. Statistics and Its Interface, 5, 345–354.

    Article  MathSciNet  Google Scholar 

  • Zhao, P., Haziza, D., & Wu, C. (2020c). Sample empirical likelihood and the design-based oracle variable selection theory. Statistica Sinica (revised).

    Google Scholar 

  • Zhao, P., & Wu, C. (2019). Some theoretical and practical aspects of empirical likelihood methods for complex surveys. International Statistical Review, 87, S239–256.

    Article  MathSciNet  Google Scholar 

  • Zhong, B., & Rao, J. N. K. (2000). Empirical likelihood inference under stratified random sampling using auxiliary population information. Biometrika, 87, 929–938.

    Article  MathSciNet  Google Scholar 

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Wu, C., Thompson, M.E. (2020). 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_8

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