The Variance Estimation of Calibration Estimators of Population Total under an Unknown Population Total for Auxiliary Variables

Sampling weights are calibrated according to the theory of calibration when the sum of population total for auxiliary variables is known. Under known population، totals for auxiliary variables and some conditions Devile and Sarndal showed that generalized regression estimators could approximate calibration estimators and their variances. In this paper، under unknown population totals for auxiliary variables، an estimator for the population total is proposed and its variance is obtained. It is shown that our estimator for the population total is more efficient than the Horvitz-Thompson estimators by theoretically and simulation results.