Two-steps variance calibrated estimators with linear and non-linear constraints for mailed surveys with non-response

This paper proposed a new class of variance estimators that uses a two-step technique with designed weights based on linear and non-linear constraints to handle the presence of non-response in sample surveys. The proposed class of the estimators has three members. It was designed to be robust against extreme values or outliers in the data. In the first step, the calibration weights of the new estimator are set proportionally to the design weights of existing finite population variance estimators for a mailed survey with non-response. In the second step, the constants of proportionality are determined based on different objectives, such as bias reduction or minimum mean squared error. This paper thoroughly examined the theoretical and numerical properties of the proposed estimators. Empirical studies using simulated data demonstrated the superior performance of two members of the proposed estimator compared to existing methods across various data scenarios. The results of the error analysis revealed that the members of the proposed class of estimator are robust and efficient.