A Goal Programming Approach for Multivariate Calibration Weights Estimation in Stratified Random Sampling

Calibration estimation is one of the most important ways to improve the precision of the survey estimates. It is a method in which the designs weights are modified as little as possible by minimizing a given distance measure to the calibrated weights respecting a set of constraints related to suitable auxiliary information. This paper proposes a new approach for Multivariate Calibration Estimation (MCE) of the population mean of a study variable under stratified random sampling scheme using two auxiliary variables. Almost all literature on calibration estimation used Lagrange multiplier technique in order to estimate the calibrated weights. While Lagrange multiplier technique requires all equations included in the model to be differentiable functions, some un- differentiable functions may be faced in some cases. Hence, it is essential to look for using another technique that can provide more flexibility in dealing with the problem. Accordingly, in this paper, using goal programming approach is newly suggested as a different approach for MCE. The theory of the proposed calibration estimation is presented and the calibrated weights are estimated. A comparison study is conducted using actual and generated data to evaluate the performance of the proposed approach for multivariate calibration estimator with other existing calibration estimators. The results of this study prove that using the proposed GP approach for MCE is more flexible and efficient compared to other calibration estimation methods of the population mean.