Estimation of Population Total Using Spline Functions

Abstract

This study sought to estimate finite population total using spline functions. The emerging patterns from spline smoother were compared with those that were obtained from the model-based, the model-assisted and the non-parametric estimators. To measure the performance of each estimator, three aspects were considered: the average bias, the efficiency by use of the average mean square error and the robustness using the rate of change of efficiency. We used six populations: four natural and two simulated. The findings showed that the model-based estimator works very well in terms of efficiency while the model-assisted is almost unbiased when the model is linear and homoscedastic. However, the estimators break down when the underlying model assumptions are violated. The Kernel Estimator (Nadaraya-Watson) is found to be the most robust of the five estimators considered. Between the two spline functions that we considered, the periodic spline was found to perform better. The spline functions were found to provide good results whether or not the design points were uniformly spaced. We also found out that, under certain conditions, a smoothing spline estimator and a Kernel estimator are equivalent. The study recommends that both the ratio estimator and the local polynomial estimator should be used within the confines of a linear homoscedastic model. The Nadaraya-Watson and the periodic spline estimators, both of which are non-parametric, are highly robust. The Nadaraya-Watson however is even more robust than the periodic spline.