Sandeep Kumar’s scientific contributions

Deville and Särndal (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 xi'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.

In the present paper we have developed calibration and model based calibration estimators of finite population total when study variable and auxiliary variable are inversely related. It has been shown that calibration, model based and model based calibration approaches provided the same estimators under certain conditions but their variances are different. A limited simulation study has been conducted to examine the relative performance of the estimators based on the aforesaid three approaches. The results of simulation study indicated that regression type model based calibration estimator is the best among all the estimators.