Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling

Kemei Anderson Kimutai; Christopher Ouma Onyango; Mike Wafula

doi:doi:10.11648/j.sjams.20210905.12

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Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling

Kemei Anderson Kimutai, Christopher Ouma Onyango, Mike Wafula

Published in Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 5)

Received: 16 September 2021 Accepted: 9 November 2021 Published: 17 November 2021

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Abstract

Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 5)
DOI	10.11648/j.sjams.20210905.12
Page(s)	126-132
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), 2024. Published by Science Publishing Group

Keywords

Finite Population Total, Missing Values, Two-phase Sampling

References

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[16]	Lehtonen, R. and Pahkinen, E. (2004). Practical Methods for Design and Analysis of Complex Surveys (2^nd Edition). New York: John Wiley & Sons Ltd.
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APA Style

Kemei Anderson Kimutai, Christopher Ouma Onyango, Mike Wafula. (2021). Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling. Science Journal of Applied Mathematics and Statistics, 9(5), 126-132. https://doi.org/10.11648/j.sjams.20210905.12

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ACS Style

Kemei Anderson Kimutai; Christopher Ouma Onyango; Mike Wafula. Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling. Sci. J. Appl. Math. Stat. 2021, 9(5), 126-132. doi: 10.11648/j.sjams.20210905.12

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AMA Style

Kemei Anderson Kimutai, Christopher Ouma Onyango, Mike Wafula. Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling. Sci J Appl Math Stat. 2021;9(5):126-132. doi: 10.11648/j.sjams.20210905.12

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@article{10.11648/j.sjams.20210905.12,
  author = {Kemei Anderson Kimutai and Christopher Ouma Onyango and Mike Wafula},
  title = {Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {5},
  pages = {126-132},
  doi = {10.11648/j.sjams.20210905.12},
  url = {https://doi.org/10.11648/j.sjams.20210905.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210905.12},
  abstract = {Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.},
 year = {2021}
}

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TY  - JOUR
T1  - Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling
AU  - Kemei Anderson Kimutai
AU  - Christopher Ouma Onyango
AU  - Mike Wafula
Y1  - 2021/11/17
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210905.12
DO  - 10.11648/j.sjams.20210905.12
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  - 126
EP  - 132
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210905.12
AB  - Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.
VL  - 9
IS  - 5
ER  -

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Author Information

Kemei Anderson Kimutai

Department of Mathematics, Kiriri Women’s University of Science and Technology, Nairobi, Kenya
Christopher Ouma Onyango

Department of Mathematics, Statistics & Actuarial Science, Kenyatta University, Nairobi, Kenya
Mike Wafula

Department of Mathematics, Statistics & Actuarial Science, Kenyatta University, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Kemei Anderson Kimutai, Christopher Ouma Onyango, Mike Wafula. (2021). Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling. Science Journal of Applied Mathematics and Statistics, 9(5), 126-132. https://doi.org/10.11648/j.sjams.20210905.12

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ACS Style

Kemei Anderson Kimutai; Christopher Ouma Onyango; Mike Wafula. Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling. Sci. J. Appl. Math. Stat. 2021, 9(5), 126-132. doi: 10.11648/j.sjams.20210905.12

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AMA Style

Kemei Anderson Kimutai, Christopher Ouma Onyango, Mike Wafula. Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling. Sci J Appl Math Stat. 2021;9(5):126-132. doi: 10.11648/j.sjams.20210905.12

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@article{10.11648/j.sjams.20210905.12,
  author = {Kemei Anderson Kimutai and Christopher Ouma Onyango and Mike Wafula},
  title = {Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {5},
  pages = {126-132},
  doi = {10.11648/j.sjams.20210905.12},
  url = {https://doi.org/10.11648/j.sjams.20210905.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210905.12},
  abstract = {Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling
AU  - Kemei Anderson Kimutai
AU  - Christopher Ouma Onyango
AU  - Mike Wafula
Y1  - 2021/11/17
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210905.12
DO  - 10.11648/j.sjams.20210905.12
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  - 126
EP  - 132
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210905.12
AB  - Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.
VL  - 9
IS  - 5
ER  -

Copy | Download