Calibration and partial calibration on principal components when the number of auxiliary variables is large

2014

In survey sampling, calibration is a very popular tool used to make total estimators consistent with known totals of auxiliary variables and to reduce variance. When the number of auxiliary variables is large, calibration on all the variables may lead to estimators of totals whose mean squared error (MSE) is larger than the MSE of the Horvitz-Thompson estimator even if this simple estimator does not take account of the available auxiliary information. We study in this paper a new technique based on dimension reduction through principal components that can be useful in this large dimension context. Calibration is performed on the first principal components, which can be viewed as the synthet…