Model-Assisted Estimation for Complex Surveys Using Penalized Splines

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalized spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. Further, they allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically normal, and they admit consistent variance estimation using familiar design-based methods. Data-driven penalty selection ∗Colorado State University, Fort Collins, CO 80523 USA; [email protected]. †K. U. Leuven, Naamsestraat 69, 3000 Leuven, Belgium; [email protected]. ‡Iowa State University, Ames, IA, 50011 USA; [email protected].