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

Jacob Oketch Okungu; George Otieno Orwa; Romanus Odhiambo Otieno

doi:doi:10.11648/j.sjams.20200802.11

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

Jacob Oketch Okungu, George Otieno Orwa, Romanus Odhiambo Otieno

Published in Science Journal of Applied Mathematics and Statistics (Volume 8, Issue 2)

Received: 6 February 2020 Accepted: 25 February 2020 Published: 23 March 2020

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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.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 8, Issue 2)
DOI	10.11648/j.sjams.20200802.11
Page(s)	35-41
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Asymptotic Normality, Nonparametric Estimator, Auxiliary Variables and Edgeworth Expansion

References

[1]	Bardoff, O. and Cox, D. R. (1979). Edgeworth and saddle point approximations with statistical applications. JROST, 41: 279–312.
[2]	Breidt, F. G. (2009). Non-Parametric Regression Estimation of Finite Population Totals Under Two-Stage Sampling. Colorado State University, Colorado.
[3]	Breidt, F. and Opsomer, P. (2005). Model-Assisted estimator for Complex Surveys using Penalized Splines. Bimetrica, volume 92, Issue 4.
[4]	Chambers, J. M. (1967). On Methods of Asymptotic Approximation for Multivariate Distributions. Biometrica, UK.
[5]	Dorfman, A. H. (1993). A comparison of design based and model-based estimators of the finite population distribution. Australian Journal of Statistics, 35: 29-41
[6]	Dorfman, A. H. (1992). Nonparametric regression for estimating totals in finite population. Journal of the American Statistical Association, 4: 622–625.
[7]	Dorfman, A. H. and Hall, P. (1992). Estimators of the finite population distribution function using nonparametric regression. 21: 1452–1475.
[8]	Efron, B. (1979). Bootstrap methods, another look at the Jackniffe. The Annals of Statistics, 10: 1–26.
[9]	Hirsen, E. B. (2009). Non Parametrics. Winconsin, New York.
[10]	Laszlo, G. A., K. M. and Walk, H. (2002). A Distribution Free-Theory of Nonparametric Regression. Springer-Verlag, New York.
[11]	Odhiambo, R. and Mwalili, S. (2000). Nonparametric regression for finite population estimation. East African Journal of Statistics, II (Part 2): 107–118.
[12]	Ombui, T. (2008). Robust Estimation of Finite Population Total Using Local Polynomial Regression. Thesis, Jomo Kenyatta University of Agriculture and Technology.
[13]	Tsybakov (2009). Intoduction to nonparametric estimation. Springer Science+Business Media, LLC, New York.
[14]	Valliant, R., Dorfman, A. and Royall (2000). Finite Population Sampling and Inference. A prediction Approach. Willey and Sons, New York.

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APA Style

Jacob Oketch Okungu, George Otieno Orwa, Romanus Odhiambo Otieno. (2020). Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion. Science Journal of Applied Mathematics and Statistics, 8(2), 35-41. https://doi.org/10.11648/j.sjams.20200802.11

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ACS Style

Jacob Oketch Okungu; George Otieno Orwa; Romanus Odhiambo Otieno. Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion. Sci. J. Appl. Math. Stat. 2020, 8(2), 35-41. doi: 10.11648/j.sjams.20200802.11

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AMA Style

Jacob Oketch Okungu, George Otieno Orwa, Romanus Odhiambo Otieno. Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion. Sci J Appl Math Stat. 2020;8(2):35-41. doi: 10.11648/j.sjams.20200802.11

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@article{10.11648/j.sjams.20200802.11,
  author = {Jacob Oketch Okungu and George Otieno Orwa and Romanus Odhiambo Otieno},
  title = {Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {8},
  number = {2},
  pages = {35-41},
  doi = {10.11648/j.sjams.20200802.11},
  url = {https://doi.org/10.11648/j.sjams.20200802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20200802.11},
  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.},
 year = {2020}
}

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TY  - JOUR
T1  - Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion
AU  - Jacob Oketch Okungu
AU  - George Otieno Orwa
AU  - Romanus Odhiambo Otieno
Y1  - 2020/03/23
PY  - 2020
N1  - https://doi.org/10.11648/j.sjams.20200802.11
DO  - 10.11648/j.sjams.20200802.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 35
EP  - 41
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20200802.11
AB  - 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.
VL  - 8
IS  - 2
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Jacob Oketch Okungu, George Otieno Orwa, Romanus Odhiambo Otieno. (2020). Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion. Science Journal of Applied Mathematics and Statistics, 8(2), 35-41. https://doi.org/10.11648/j.sjams.20200802.11

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ACS Style

Jacob Oketch Okungu; George Otieno Orwa; Romanus Odhiambo Otieno. Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion. Sci. J. Appl. Math. Stat. 2020, 8(2), 35-41. doi: 10.11648/j.sjams.20200802.11

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AMA Style

Jacob Oketch Okungu, George Otieno Orwa, Romanus Odhiambo Otieno. Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion. Sci J Appl Math Stat. 2020;8(2):35-41. doi: 10.11648/j.sjams.20200802.11

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@article{10.11648/j.sjams.20200802.11,
  author = {Jacob Oketch Okungu and George Otieno Orwa and Romanus Odhiambo Otieno},
  title = {Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {8},
  number = {2},
  pages = {35-41},
  doi = {10.11648/j.sjams.20200802.11},
  url = {https://doi.org/10.11648/j.sjams.20200802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20200802.11},
  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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion
AU  - Jacob Oketch Okungu
AU  - George Otieno Orwa
AU  - Romanus Odhiambo Otieno
Y1  - 2020/03/23
PY  - 2020
N1  - https://doi.org/10.11648/j.sjams.20200802.11
DO  - 10.11648/j.sjams.20200802.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 35
EP  - 41
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20200802.11
AB  - 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.
VL  - 8
IS  - 2
ER  -

Copy | Download