Two Levels Model Calibration in Cluster Sampling; Use of Penalized Splines in Semiparametric Estimation

Estimation of finite population total using internal calibration and model assistance on semiparametric models based on kernel methods have been considered by several authors. In this paper, we have extended this to consider model calibration based on penalized splines in two stage sampling where the auxiliary information is available both at the element level and at the cluster level. We have shown that the proposed estimators are robust in the face of misspecified models, are asymptotic design unbiased, have reduced model bias, are consistent and asymptotic normal. We have shown that estimators based on penalized splines perform better than corresponding kernel based estimators and model calibrated estimators perform better than internally calibrated estimators do. . Keywords: model assistance, model calibration, semiparametric model, penalized spline