B-Spline Estimation in a Survey Sampling Framework

Nonparametric regression models have been used more and more over the last years to model survey data and incorporate efficiently auxiliary information in order to improve the estimation of totals, means or other study parameters such as Gini index or poverty rate. B-spline nonparametric regression has the benefit of being very flexible in modeling nonlinear survey data while keeping many similarities and properties of the classical linear regression. This method proved to be efficient for deriving a unique system of weights which allowed to estimate in an efficient way and simultaneously many study parameters. Applications on real and simulated survey data showed its high efficiency. This paper aims at giving a review of applications of the B-spline nonparametric regression in a survey sampling framework and design-based approach. Handling item nonresponse by B-spline modeling is also considered. This review includes also new properties and improved consistency rates of the suggested penalized and unpenalized B-spline estimators.