Abstract
This study explores the estimation of finite population total. For many years design-based approach dominated the scene in statistical inference in sample surveys. The scenario has since changed with emergence of the other approaches (Model-Based, Model-Assisted and the Randomization-Assisted), which have proved to rival the conventional approach. This paper focuses on a model based approach. Within this framework a nonparametric regression estimator for finite population total is developed. The nonparametric technique has been found from previous studies to be advantageous than its parametric counterpart in terms of robustness and flexibility.  Kernel smoother has been used in construction of the estimator. The challenge of the boundary problem encountered with the Nadaraya-Watson estimator has been addressed by modifying it using reflection technique. The performance of the proposed estimator has been compared to the design-based Horvitz Thompson estimator and the model –based nonparametric regression estimator proposed by (Dorfman, 1992) and the ratio estimator using simulated data.
Highlights
Background and MotivationThe goal of a researcher in survey sampling is to make estimation of the population parameters with precision and accuracy
Suppose we have a finite population of N distinct and identifiable units; U 1, 2,..., N
This study explores the estimation of finite population total
Summary
The goal of a researcher in survey sampling is to make estimation of the population parameters with precision and accuracy. Auxiliary information on finite population is often used to increase precision of estimators of parameters, (Cochran, 1977). A linear regression estimate may produce a large error for every sample size if the true underlying function is not linear and cannot be well approximated by a linear function (Lászlό, A, Kohler, & Walk, 2002). To address this problem the non parametric regression estimation is the option to go for. Nonparametric estimation that use kernel densities, suffer from the boundary bias
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