Two-Step Calibrated Designed Weighted Estimators of Finite Population Variance for a Mailed Survey Design Characterized by Non-response

In this paper, a new class of variance estimators based on a two-step designed weights technique in the presence of non-response is proposed. The proposed estimator is designed to be robust against extreme values or outliers. In the first step, the calibration weights of the new class of estimators are set proportional to the design weights of the existing finite population variance estimator for a mailed survey design characterized by the presence of non-response. In the second step, the constants of proportionality are determined based on different objectives of the investigator such as bias reduction or minimum mean squared error. Many estimators available in the literature can be shown to be special cases of the proposed two-step calibrated estimator. The properties of the proposed estimators are studied theoretically and numerically. Empirical studies were conducted using ten simulated data to illustrate the performance of proposed estimators over existing ones. The results of the numerical comparison depicted the superiority of two members of the proposed estimator in all cases of data considered.