Non-Parametric Estimator for a Finite Population Total Under Stratified Sampling Incorporating a Hybrid of Data Transformation and Reflection Techniques

Abstract

Survey sampling methods are used in the estimation of population parameters of interest. This field has received increased demand due to the reliable statistics they produce. Information is extracted from the samples and used to make inferences about the population. In this paper, a nonparametric estimator for a finite population total that addresses the problem of boundary bias is proposed. The properties of this estimator were studied in order to determine its accuracy. The estimator was applied to a simulated data and the analysis was done using R statistical package version i386 4.0.3 and the results of the bias confirmed. The performance of the proposed estimator was tested and compared to the design-based Horvitz-Thompson estimator, the model-based approach proposed by Dorfman and the ratio estimator. This was done by studying both the unconditional and conditional properties of the estimators under the linear, quadratic and exponential mean functions. The proposed estimator outperformed other estimators in quadratic and exponential mean functions and therefore can be recommended for estimation and addressing the boundary problem.

Keywords: data transformation, data reflection, boundary bias