Randomized Principal Component Ensembles for High-Dimensional Calibration
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 an ensemble method based on a principal component decomposition of the auxiliary variables. We repeatedly select sets of principal components without replacement and with unequal selection probabilities. Calibration is performed on each selected set of principal components, and the resulting weights are aggregated to obtain a final set of weights. With our proposed method, it is possible to calibrate exactly for some of the main auxiliary variables, while relaxing the calibration constraints for the remaining variables. It yields a total estimator whose variance does not explode when new auxiliary variables are added while producing weights with low dispersion. Finally, our proposed method allows us to obtain a single weighting system that can be applied to several variables of interest of a survey. An estimator of the variance of the total estimator is also proposed. We evaluate the proposed total estimator and its variance estimator using a simulation study on real survey data from the Swiss Survey on Income and Living Conditions and on synthetic data. The results show that the proposed solution significantly reduces the weight variability and the variance of the total estimator compared with competing total estimators for some variables of interest.