Variance reduction in surveys with auxiliary information: a nonparametric approach involving regression splines

The author considers the use of auxiliary information available at population level to improve the estimation of finite population totals. She introduces a new type of model-assisted estimator based on nonparametric regression splines. The estimator is a weighted linear combination of the study variable with weights calibrated to the B-splines known population totals. The author shows that the estimator is asymptotically design-unbiased and consistent under conditions which do not require the superpopulation model to be correct. She proposes a design-based variance approximation and shows that the anticipated variance is asymptotically equivalent to the Godambe-Joshi lower bound. She also shows through simulations that the estimator has good properties.