Several writers have studied internal calibration and model help on semiparametric models based on kernel methods for estimating finite population totals. We extend this in this book chapter to investigate model calibration using penalised splines in two-stage sampling with auxiliary information provided at both the element and cluster levels. In particular, we derive population total estimators that take model calibration into account when estimating cluster totals and estimating population total. We show that the suggested estimators are robust in the face of misspecified models, have decreased model bias, are design consistent, and are asymptotic normal. We have demonstrated that estimators based on penalised splines outperform kernel-based estimators, and that model calibrated estimators outperform internally calibrated estimators.
Pius Nderitu Kihara
Department of Financial and Actuarial Mathematics, Technical University of Kenya, Kenya.