Abstract: Calibration estimation, which can be roughly described as a method of adjusting the original design weights to incorporate the known population totals of the auxiliary variables, has become very popular in sample surveys. The calibration weights are chosen to minimize a given distance measure while satisfying a set of constraints related to the auxiliary variable information. Under simple random sampling, Chen and Qin (1993) suggested that the calibration estimator maximizing the constrained empirical likelihood can make efficient use of the auxiliary variables. We extend the result to unequal probability sampling and propose an algorithm to implement the proposed procedure. Asymptotic properties of the proposed calibration estimator are discussed. The proposed method is extended to the stratified sampling. Results from a limited simulation study are presented.
Key words and phrases: Generalized regression estimator, nonparametric maximum likelihood estimator, optimal regression estimator, weighting procedure.