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Semiparametric analysis in double-sampling designs via empirical likelihood

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  • Yu, Wen

Abstract

Double-sampling designs are commonly used in real applications when it is infeasible to collect exact measurements on all variables of interest. Two samples, a primary sample on proxy measures and a validation subsample on exact measures, are available in these designs. We assume that the validation sample is drawn from the primary sample by the Bernoulli sampling with equal selection probability. An empirical likelihood based approach is proposed to estimate the parameters of interest. By allowing the number of constraints to grow as the sample size goes to infinity, the resulting maximum empirical likelihood estimator is asymptotically normal and its limiting variance-covariance matrix reaches the semiparametric efficiency bound. Moreover, the Wilks-type result of convergence to chi-squared distribution for the empirical likelihood ratio based test is established. Some simulation studies are carried out to assess the finite sample performances of the new approach.

Suggested Citation

  • Yu, Wen, 2011. "Semiparametric analysis in double-sampling designs via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1302-1314, October.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:9:p:1302-1314
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    References listed on IDEAS

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    1. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    2. 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.
    3. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
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