High-dimensional estimation in a survey sampling framework, model-assisted and calibration points of view
摘要
In surveys, model-assisted estimators and calibration estimators, based on auxiliary information, are commonly used to obtain efficient estimators of population totals/means. Nowadays, it is no longer unusual to face high-dimensional auxiliary information. Incorporating too many auxiliary variables in model-assisted and calibration estimators may lead to a loss of efficiency. In this paper, I will discuss the asymptotic efficiency of model-assisted and calibration estimators based on high-dimensional auxiliary data and show that they may suffer from an additional variability in certain conditions. I will also present two techniques for improving the efficiency of model-assisted and calibration estimators in a high-dimensional framework: the first one is based on ridge-type penalization and the second one is based on dimension reduction through principal components.