Nonparametric Estimation of Finite Population Total

Abstract

In this study, the problem of nonparametric estimation of finite population total using multiplicative bias correction technique is considered. A review of the model-based, design-based, model-assisted, randomization-assisted and nonparametric approaches to finite population total estimation is explored. A robust estimator of the finite population total based on multiplicative bias correction is derived. The properties of the estimator are developed and comparative study with the existing model based and design based estimators is carried to assess the performance of the estimator developed using the simulated sets of data. It is observed that the estimator is asymptotically unbiased and statistically consistent when certain conditions are satisfied. It has been shown that when the model based estimators are used in estimating the finite population total, there exists bias-variance trade-off along the boundary. The multiplicative bias corrected estimator has recorded better results in estimating the finite population total by correcting the boundary problems associated with existing model based estimators. The theoretical and empirical results led to the suggestion that the multiplicative bias corrected estimator can be highly recommended in survey sampling estimation of the finite population total.