Calibration with Bagging of the Principal Components on a Large Number of Auxiliary Variables

Abstract: Calibration is a widely used method in survey sampling to adjust weights so that estimated totals of some chosen calibration variables match known population totals or totals obtained from other sources. When a large number of auxiliary variables are included as calibration variables, the variance of the total estimator can increase, and the calibration weights can become highly dispersed. To address these issues, we propose a solution inspired by bagging and principal component decomposition. With our approach, the principal components of the auxiliary variables are constructed. Several samples of calibration variables are selected without replacement and with unequal probabilities from among the principal components. For each sample, a system of weights is obtained. The final weights are the average weights of these different weighting systems. With our proposed method, it is possible to calibrate exactly for some of the main auxiliary variables. For the other auxiliary variables, the weights cannot be calibrated exactly. The proposed method allows us to obtain a total estimator whose variance does not explode when new auxiliary variables are added and to obtain very low scatter weights. Finally, our proposed method allows us to obtain a single weighting system that can be applied to several variables of interest of a survey.