Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error

Ikechukwu Boniface Okafor; Chukwudi Justin Ogbonna; Lawrence Chizoba Kiwu; Chinnyeaka Hostensia Izunobi; Fidelia Kiwu-Lawrence

doi:doi:10.11648/j.sf.20220303.12

Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error

Ikechukwu Boniface Okafor, Chukwudi Justin Ogbonna, Lawrence Chizoba Kiwu, Chinnyeaka Hostensia Izunobi, Fidelia Kiwu-Lawrence

Published in Science Frontiers (Volume 3, Issue 3)

Received: 15 July 2022 Accepted: 1 August 2022 Published: 31 August 2022

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Abstract

In this paper log transformation of modified ratio estimator of population mean when non-response error exists on both study variable and auxiliary variable was proposed. Using sub-sampling method of treating unit non-response, the properties of the proposed estimator as well as optimality conditions up to first order approximation were obtained. Theoretical and empirical comparison of the proposed estimator were carried out, comparing it with some existing estimators. The result of the theoretical comparison shows that the proposed estimator under optimum condition is more efficient than classical ratio estimator and Hansen and Hurwitz unbiased estimator. Furthermore, the empirical analysis on two different datasets revealed that the mean squared error of the proposed estimator increases as the value of λ increases. Also the percentage relative efficiency increases with the increase in the value of λ. The theoretical results are in consonant with the empirical results hence the proposed estimator is considered more efficient than classical ratio and Hansen and Hurwitz unbiased estimators in terms having lower mean squared error and more gain in efficiency under optimality condition in estimating population mean in the presence of non-response error and can be used in real life survey.

Published in	Science Frontiers (Volume 3, Issue 3)
DOI	10.11648/j.sf.20220303.12
Page(s)	106-111
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), 2022. Published by Science Publishing Group

Keywords

Log Transformation, Modified Ratio Estimator, Optimality Conditions, Sub-sampling, Unit Non-response

References

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APA Style

Ikechukwu Boniface Okafor, Chukwudi Justin Ogbonna, Lawrence Chizoba Kiwu, Chinnyeaka Hostensia Izunobi, Fidelia Kiwu-Lawrence. (2022). Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error. Science Frontiers, 3(3), 106-111. https://doi.org/10.11648/j.sf.20220303.12

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ACS Style

Ikechukwu Boniface Okafor; Chukwudi Justin Ogbonna; Lawrence Chizoba Kiwu; Chinnyeaka Hostensia Izunobi; Fidelia Kiwu-Lawrence. Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error. Sci. Front. 2022, 3(3), 106-111. doi: 10.11648/j.sf.20220303.12

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AMA Style

Ikechukwu Boniface Okafor, Chukwudi Justin Ogbonna, Lawrence Chizoba Kiwu, Chinnyeaka Hostensia Izunobi, Fidelia Kiwu-Lawrence. Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error. Sci Front. 2022;3(3):106-111. doi: 10.11648/j.sf.20220303.12

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@article{10.11648/j.sf.20220303.12,
  author = {Ikechukwu Boniface Okafor and Chukwudi Justin Ogbonna and Lawrence Chizoba Kiwu and Chinnyeaka Hostensia Izunobi and Fidelia Kiwu-Lawrence},
  title = {Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error},
  journal = {Science Frontiers},
  volume = {3},
  number = {3},
  pages = {106-111},
  doi = {10.11648/j.sf.20220303.12},
  url = {https://doi.org/10.11648/j.sf.20220303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sf.20220303.12},
  abstract = {In this paper log transformation of modified ratio estimator of population mean when non-response error exists on both study variable and auxiliary variable was proposed. Using sub-sampling method of treating unit non-response, the properties of the proposed estimator as well as optimality conditions up to first order approximation were obtained. Theoretical and empirical comparison of the proposed estimator were carried out, comparing it with some existing estimators. The result of the theoretical comparison shows that the proposed estimator under optimum condition is more efficient than classical ratio estimator and Hansen and Hurwitz unbiased estimator. Furthermore, the empirical analysis on two different datasets revealed that the mean squared error of the proposed estimator increases as the value of λ increases. Also the percentage relative efficiency increases with the increase in the value of λ. The theoretical results are in consonant with the empirical results hence the proposed estimator is considered more efficient than classical ratio and Hansen and Hurwitz unbiased estimators in terms having lower mean squared error and more gain in efficiency under optimality condition in estimating population mean in the presence of non-response error and can be used in real life survey.},
 year = {2022}
}

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TY  - JOUR
T1  - Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error
AU  - Ikechukwu Boniface Okafor
AU  - Chukwudi Justin Ogbonna
AU  - Lawrence Chizoba Kiwu
AU  - Chinnyeaka Hostensia Izunobi
AU  - Fidelia Kiwu-Lawrence
Y1  - 2022/08/31
PY  - 2022
N1  - https://doi.org/10.11648/j.sf.20220303.12
DO  - 10.11648/j.sf.20220303.12
T2  - Science Frontiers
JF  - Science Frontiers
JO  - Science Frontiers
SP  - 106
EP  - 111
PB  - Science Publishing Group
SN  - 2994-7030
UR  - https://doi.org/10.11648/j.sf.20220303.12
AB  - In this paper log transformation of modified ratio estimator of population mean when non-response error exists on both study variable and auxiliary variable was proposed. Using sub-sampling method of treating unit non-response, the properties of the proposed estimator as well as optimality conditions up to first order approximation were obtained. Theoretical and empirical comparison of the proposed estimator were carried out, comparing it with some existing estimators. The result of the theoretical comparison shows that the proposed estimator under optimum condition is more efficient than classical ratio estimator and Hansen and Hurwitz unbiased estimator. Furthermore, the empirical analysis on two different datasets revealed that the mean squared error of the proposed estimator increases as the value of λ increases. Also the percentage relative efficiency increases with the increase in the value of λ. The theoretical results are in consonant with the empirical results hence the proposed estimator is considered more efficient than classical ratio and Hansen and Hurwitz unbiased estimators in terms having lower mean squared error and more gain in efficiency under optimality condition in estimating population mean in the presence of non-response error and can be used in real life survey.
VL  - 3
IS  - 3
ER  -

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Author Information

Ikechukwu Boniface Okafor

Department of Statistics, Covenant Polytechnic, Aba, Nigeria
Chukwudi Justin Ogbonna

Department of Statistics, Federal University of Technology, Owerri, Nigeria
Lawrence Chizoba Kiwu

Department of Statistics, Federal University of Technology, Owerri, Nigeria
Chinnyeaka Hostensia Izunobi

Department of Statistics, Federal University of Technology, Owerri, Nigeria
Fidelia Kiwu-Lawrence

Department of Statistics, Abia State University, Uturu, Nigeria

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APA Style

Ikechukwu Boniface Okafor, Chukwudi Justin Ogbonna, Lawrence Chizoba Kiwu, Chinnyeaka Hostensia Izunobi, Fidelia Kiwu-Lawrence. (2022). Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error. Science Frontiers, 3(3), 106-111. https://doi.org/10.11648/j.sf.20220303.12

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ACS Style

Ikechukwu Boniface Okafor; Chukwudi Justin Ogbonna; Lawrence Chizoba Kiwu; Chinnyeaka Hostensia Izunobi; Fidelia Kiwu-Lawrence. Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error. Sci. Front. 2022, 3(3), 106-111. doi: 10.11648/j.sf.20220303.12

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AMA Style

Ikechukwu Boniface Okafor, Chukwudi Justin Ogbonna, Lawrence Chizoba Kiwu, Chinnyeaka Hostensia Izunobi, Fidelia Kiwu-Lawrence. Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error. Sci Front. 2022;3(3):106-111. doi: 10.11648/j.sf.20220303.12

Copy | Download

@article{10.11648/j.sf.20220303.12,
  author = {Ikechukwu Boniface Okafor and Chukwudi Justin Ogbonna and Lawrence Chizoba Kiwu and Chinnyeaka Hostensia Izunobi and Fidelia Kiwu-Lawrence},
  title = {Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error},
  journal = {Science Frontiers},
  volume = {3},
  number = {3},
  pages = {106-111},
  doi = {10.11648/j.sf.20220303.12},
  url = {https://doi.org/10.11648/j.sf.20220303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sf.20220303.12},
  abstract = {In this paper log transformation of modified ratio estimator of population mean when non-response error exists on both study variable and auxiliary variable was proposed. Using sub-sampling method of treating unit non-response, the properties of the proposed estimator as well as optimality conditions up to first order approximation were obtained. Theoretical and empirical comparison of the proposed estimator were carried out, comparing it with some existing estimators. The result of the theoretical comparison shows that the proposed estimator under optimum condition is more efficient than classical ratio estimator and Hansen and Hurwitz unbiased estimator. Furthermore, the empirical analysis on two different datasets revealed that the mean squared error of the proposed estimator increases as the value of λ increases. Also the percentage relative efficiency increases with the increase in the value of λ. The theoretical results are in consonant with the empirical results hence the proposed estimator is considered more efficient than classical ratio and Hansen and Hurwitz unbiased estimators in terms having lower mean squared error and more gain in efficiency under optimality condition in estimating population mean in the presence of non-response error and can be used in real life survey.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Log Transformation of Modified Ratio Estimator in the Presence of Non-Response Error
AU  - Ikechukwu Boniface Okafor
AU  - Chukwudi Justin Ogbonna
AU  - Lawrence Chizoba Kiwu
AU  - Chinnyeaka Hostensia Izunobi
AU  - Fidelia Kiwu-Lawrence
Y1  - 2022/08/31
PY  - 2022
N1  - https://doi.org/10.11648/j.sf.20220303.12
DO  - 10.11648/j.sf.20220303.12
T2  - Science Frontiers
JF  - Science Frontiers
JO  - Science Frontiers
SP  - 106
EP  - 111
PB  - Science Publishing Group
SN  - 2994-7030
UR  - https://doi.org/10.11648/j.sf.20220303.12
AB  - In this paper log transformation of modified ratio estimator of population mean when non-response error exists on both study variable and auxiliary variable was proposed. Using sub-sampling method of treating unit non-response, the properties of the proposed estimator as well as optimality conditions up to first order approximation were obtained. Theoretical and empirical comparison of the proposed estimator were carried out, comparing it with some existing estimators. The result of the theoretical comparison shows that the proposed estimator under optimum condition is more efficient than classical ratio estimator and Hansen and Hurwitz unbiased estimator. Furthermore, the empirical analysis on two different datasets revealed that the mean squared error of the proposed estimator increases as the value of λ increases. Also the percentage relative efficiency increases with the increase in the value of λ. The theoretical results are in consonant with the empirical results hence the proposed estimator is considered more efficient than classical ratio and Hansen and Hurwitz unbiased estimators in terms having lower mean squared error and more gain in efficiency under optimality condition in estimating population mean in the presence of non-response error and can be used in real life survey.
VL  - 3
IS  - 3
ER  -

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