Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion

Abstract

In survey sampling, the main objective is to make inference about the entire population parameters using the sample statistics. In this study, a nonparametric estimator of finite population total is proposed and the coverage probabilities using the Edgeworth expansion explored. Three properties; unbiasedness, efficiency and the confidence interval of the proposed estimator are studied. There is a lot of literature on study of two properties; unbiasedness and efficiency of the finite population total. This study therefore has more focus on confidence interval and coverage probability. The amount of bias and MSE are studied partially analytically, followed by an empirical study on the two properties and the confidence interval of the proposed estimator. Based on the empirical study with simulations in R, the proposed estimator resulted into smaller bias and MSE compared to the nonparametric estimator due to [6], the design-based Horvitz-Thompson estimator and the model-based ratio estimator. Further, the proposed estimator is tighter compared to the other three considered in this study and has higher converging coverage probabilities.