Volume 8, Issue 2, April 2020, Page: 35-41
Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion
Jacob Oketch Okungu, Department of Mathematics, School of Pure and Applied Sciences, Meru University of Science and Technology (MUST), Meru, Kenya
George Otieno Orwa, Department of Statistics and Actuarial Sciences, School of Mathematical Sciences, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
Romanus Odhiambo Otieno, Department of Mathematics, School of Pure and Applied Sciences, Meru University of Science and Technology (MUST), Meru, Kenya
Received: Feb. 6, 2020;       Accepted: Feb. 25, 2020;       Published: Mar. 23, 2020
DOI: 10.11648/j.sjams.20200802.11      View  387      Downloads  142
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.
Keywords
Asymptotic Normality, Nonparametric Estimator, Auxiliary Variables and Edgeworth Expansion
To cite this article
Jacob Oketch Okungu, George Otieno Orwa, Romanus Odhiambo Otieno, Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion, Science Journal of Applied Mathematics and Statistics. Vol. 8, No. 2, 2020, pp. 35-41. doi: 10.11648/j.sjams.20200802.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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