On various approaches for estimating finite population total in survey sampling under ratio super population model

Deville and S'rndal (1992) developed calibration estimator by using the auxiliary information to obtain a better estimate of the population total of study variate y. While calibration approach does not assume any explicit relationship between y and x but it assumes that only X, the population total of x is known. Prediction approach advocated by Royall and Herson (1973) leads to model based estimator of finite population under a assumption of specified super population model where x i's are supposed to be known for all i = 1, 2, 3, ..., N. Wu and Sitter (2001) proposed a design oriented model based calibration estimator of population total, when they also assumed that Xi are known for all i = 1, 2, 3, ..., N. It has been shown that these three approaches i.e. calibration approach, model based approach and model based calibration approach provides the same estimator under some situation. However, their variances are different. In the present paper, an attempt has been made to conduct a limited simulation study to examine the relative performance of the estimators based on the aforesaid three approaches. From the results of the simulation study, it has been found that calibration estimates are best.