Variance estimation of survey estimates calibrated on estimated control total: an application to the extended regression estimator and the regression composite estimator

Calibration on control totals is commonly used for survey weighting. It is usually assumed that these totals are values known without sampling errors. However, they can be estimated from other sources. A variance estimator that takes into account the randomness of control totals is derived. Several situations such as calibration on external sources and calibration with sampling on two occasions are investigated. The methodology proposed is general and can be implemented in various situations when control totals are estimated