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An empirical likelihood approach to data analysis under two-stage sampling designs

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  • Zheng, Ming
  • Yu, Wen

Abstract

A new empirical likelihood approach is developed to analyze data from two-stage sampling designs, in which a primary sample of rough or proxy measures for the variables of interest and a validation subsample of exact information are available. The validation sample is assumed to be a simple random subsample from the primary one. The proposed empirical likelihood approach is capable of utilizing all the information from both the specific models and the two available samples flexibly. It maintains some nice features of the empirical likelihood method and improves the asymptotic efficiency of the existing inferential procedures. The asymptotic properties are derived for the new approach. Some numerical studies are carried out to assess the finite sample performance.

Suggested Citation

  • Zheng, Ming & Yu, Wen, 2011. "An empirical likelihood approach to data analysis under two-stage sampling designs," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 947-956, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:947-956
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    References listed on IDEAS

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    1. Yi‐Hau Chen & Hung Chen, 2000. "A unified approach to regression analysis under double‐sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 449-460.
    2. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    3. Qihua Wang & J. N. K. Rao, 2002. "Empirical Likelihood‐based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 563-576, September.
    4. Stute, Winfried & Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood Inference in Nonlinear Errors-in-Covariables Models With Validation Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 332-346, March.
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    1. Vexler, Albert & Zou, Li & Hutson, Alan D., 2019. "The empirical likelihood prior applied to bias reduction of general estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 96-106.
    2. Yu, Wen, 2011. "Semiparametric analysis in double-sampling designs via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1302-1314, October.

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