The extended nested-error regression model with penalized spline function for estimation under informative sampling

Abstract

Model-based estimates have been developed in statistics. Often, the statisticians use the data that obtained through complex sampling designs for estimation. If the probability of inclusion in the sampling design is informative, then the informativeness of sampling must be taken into account in the estimation process. We extended the nested error regression model at the unit level by adding the probability of inclusion as a covariate in the model but with an unknown functional form to reduce the informativeness effect. This extended part in the model is then approached using a penalized spline function. In the mixed model framework, we derived the EBLUP estimator for the mean areas of population. A simulation is given to applying this approach by using the first order of the p-spline function. The RMSPE value and the average absolute bias value obtained through the use of the bootstrap method then compared with that results from the approach using the nested error regression model.