The prediction model, which makes effective use of auxiliary information available throughout the population, is often used to derive efficient estimation in survey sampling. To protect against failure of the assumed model, asymptotic design unbiasedness is often imposed in the prediction estimator. An instrumental-variable calibration estimator can be considered to achieve the model optimality among the class of calibration estimators that is asymptotically design unbiased. In this paper, we propose a new calibration estimator that is asymptotically equivalent to the optimal instrumental-variable calibration estimator. The resulting weights are no smaller than one and can be constructed to achieve the range restrictions. The proposed method can be extended to calibration estimation under two-phase sampling. Some numerical results are presented using the data from the 1997 National Resource Inventory of the United States.
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