A Dual Problem of Calibration of Design Weights Based on Multi-Auxiliary Variables

Singh (2013) considered the dual problem to the calibration of design weights to obtain a new generalized linear regression estimator (GREG) for the finite population total. In this work, we have made an attempt to suggest a way to use the dual calibration of the design weights in case of multi-auxiliary variables; in other words, we have made an attempt to give an answer to the concern in Remark 2 of Singh (2013) work. The same idea is also used to generalize the GREG estimator proposed by Deville and S$\ddot{a}$rndal (1992). It is not an easy task to find the optimum values of the parameters appear in our approach; therefore, few suggestions are mentioned to select values for such parameters based on a random sample. Based on real data set and under simple random sampling without replacement design, our approach is compared with other approaches mentioned in this paper and for different sample sizes. Simulation results show that all estimators have negligible relative bias, and the multivariate case of Singh (2013) estimator is more efficient than other estimators.