Réduction de la variance dans les sondages en présence d'information auxiliarie: Une approache non paramétrique par splines de régression

Abstract

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.