Robust Estimation of Finite Population Total Incorporating Data-Reflection Technique in Nonparametric Regression

Abstract

For planning purposes, accurate information regarding population parameters of interest is essential. This information can be obtained through census or survey sampling. In sample surveys, the sampling estimation employed in a research is important since it determines the degree of accuracy. Estimation can be parametric where pre-determined parameters have been utilized or otherwise nonparametric. In nonparametric estimation, the standard kernel smoothing function has been known to suffer from the boundary bias. To overcome this, a modified kernel smoother that does not suffer significantly from this boundary effect has been proposed. This approach was found appropriate since it allows both robustness and optimality to be achieved. These properties of the proposed estimator have been investigated and the characteristics of robustness and optimality confirmed. The estimator has also been compared with the ratio estimator, the standard Nadaraya-Watson estimator as well as the design-based Horvitz-Thompson estimator using relative bias. Further to this, the Mean Square Error (MSE) as well as conditional biases were also computed to gauge the performance of the estimators. The properties of the estimators were investigated empirically and comparative analysis was made using simulated data. It is shown that the finite population total estimator whose kernel smoother was modified using reflection technique significantly addresses the bias at the boundary. This was evident from the smaller values of MSE and narrower confidence intervals, noted in the study. The relative biases also supported these findings. The study showed that the proposed estimator generally performs better than the other estimators considered.