Estimation of Finite Population Total in the Face of Missing Values Using Model Calibration and Model Assistance on Semiparametric and Nonparametric Models

Abstract

Estimation of nite population total using model calibration and model assistance on semiparametric and nonparametric models and in the presence of auxilliary information is considered. In particular, a class of estimators based on penalized splines are proposed for one stage and two stage sampling. Firstly, estimation of nite population total using internal calibration, model calibration and model assistance on nonparametric models based on kernel methods have been consid- ered by several authors. We have considered such model calibration and model assistance estimation based on penalized splines and extended the estimation to two stage sampling. Secondly, estimation of nite population total using inter- nal calibration and model assistance on semiparametric models based on kernel methods have also been considered by several authors. In this thesis, we have extended this to consinder model calibration, based the estimation on penalized splines and extended the estimation to two stage sampling consindering two sce- narios. In the rst scenario, the auxilliary information is only available at the cluster level and in the second scenario, the auxilliary information is available both at the element level and at the cluster level. We have shown that the pro- posed estimators are robust in the face of misspeci ed 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 while model calibrated estimators perform better than internally calibrated estimators. We also recommend some areas for further research.