Results on Robust Model Based Estimation in Finite Populations

Abstract

In this article, we present results on nonparametric regression for estimating unknown finite population totals in a model based framework. Consistent robust estimators of finite population totals are derived using the procedure of local polynomial regression and their robustness properties studied (see Kikechi et al (2017), Kikechi et al (2018) and Kikechi and Simwa (2018)). Results of the bias show that the Local Polynomial estimators dominate the Horvitz-Thompson estimator for the linear, quadratic, bump and jump populations. Further, the biases under the model based Local Polynomial approach are much lower than those under the design based Horvitz-Thompson approach in different populations. The MSE results show that the Local Linear Regression estimators are performing better than the Horvitz-Thompson and Dorfman estimators, irrespective of the model specification or misspecification. Results further indicate that the confidence intervals generated by the model based Local Polynomial procedure are much tighter than those generated by the design based Horvitz-Thompson method, regardless of whether the model is specified or misspecified. It has been observed that the model based approach outperforms the design based approach at 95% coverage rate. In terms of their efficiency, and in comparison with other estimators that exist in the literature, it is observed that the Local Polynomial Regression estimators are robust and are the most efficient estimators. Generally, the Local Polynomial Regression estimators are not only superior to the popular Kernel Regression estimators, but they are also the best among all linear smoothers including those produced by orthogonal series and spline methods. The estimators adapt well to bias problems at boundaries and in regions of high curvature and they do not require smoothness and regularity conditions required by other methods such as the boundary Kernels.