| Peer-Reviewed

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

Received: 15 July 2022     Accepted: 1 August 2022     Published: 31 August 2022
Views:       Downloads:
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
[1] Bhushan S., Pandey A. P.(2018): Optimality of Ratio Type Estimation Methods for Population Mean in the Presence of Missing Data. Common Statistics Theory Methods, 47 (11), Pp. 2576–2589.
[2] Boniface Ikechukwu Okafor, Onyeka Chijioke Alyosius, Ogbonna Justin Chukwudi, Izunobi Chinyeaka Hostensia (2022): Effect of Correlated Measurement Errors on Estimation of Population Mean with Modified Ratio Estimator. Biom Biostat Int J.; 11 (2): 52‒56.
[3] Chaudhary M. K., Kumar A. (2015): Estimating the Population Mean in Stratified Random Sampling using Two-Phase Sampling in the Presence of Non-Response. World Applied Sciences Journal. Vol. 33, Issue 6, Pp. 874 – 882.
[4] Ceren Unal, Cem Kadilar (2022): A New Population Mean Estimator under Non-Response Cases. Journal of Taibah University for Science. Vol. 16, No. 1, pp. 111 – 119.
[5] Ceren Unal, Cem Kadilar (2019): Exponential Type Estimator for the Population Mean in the Presence of Non-Response. Journal of Statistics and Management Systems, DOI: 10.1080/09720510.2019.1668158.
[6] Ceren Unal, Cem Kadilar (2021): A New Family of Exponential Type Estimators in the Presence of Non-Response. J. Math. Fund. Sci. Vol. 53, No. 1, pp. 1 – 15.
[7] Dansawad N. (2019): A Class of Exponential Estimator to Estimate the Population Mean in the Presence of Non-Response. Naresuan Univ. J. Sci. Techn. 27 (4): 20 – 26.
[8] Hansen M. H., Hurwitz W. N. (1946): The Problem of Non-Response in Sample Survey. J. Am Stat Assoc. 41 (236): Pp. 517 – 529.
[9] Izunobi Chinyeaka Hostensia, Onyeka Aloysius Chijioke (2019): Logarithmic Ratio and Product-Type Estimators of Population Mean in Simple Random Sampling. International Journal of Advanced Statistics and Probability, 7 (2) Pp. 47-55.
[10] Khare B. B., Sinha R. R. (2009): On Class of Estimators for Population Mean Using Multi-Auxiliary Characters in the Presence of Non-Response. Statistics in Transition, 10 (1), pp. 3 – 14.
[11] Khare B. B., Srivastava S. (1997): Transformed ratio type estimators for the Population Mean in the Presence of Non-Response. Communications in Statistics – Theory and Methods, 26 (7), Pp. 1779 – 1791.
[12] Kumar S. (2013): Improved Exponential Estimator for Estimation of Population Mean in the Presence of Non-Response. Communication Statistics Application Methods. 20 (5): Pp. 357 – 366.
[13] Kumar S., Bhougal S. (2011): Estimation of the Population Mean in the Presence of Non-Response. Communication Statistics Application Methods. 20 (5): Pp. 357 – 366.
[14] Okafor F. C: (2001): Treatment of Non-Response in Successive Sampling. STATISTICA, anno LXI, n. 2.
[15] Onyeka A. C., Ogbumuo D. T., Izunobi C. H. (2019): Estimation of Population Mean in Stratified Random Sampling when using Auxiliary Information in the Presence of Non-Response.
[16] Rajesh Singh, Madhulika Mishra, Madhulika Mishra (2020): Estimation in Stratified Random Sampling in the Presence Of Errors. REVISTA INVESTIGACION OPERACIONAL VOL. 41, NO. 1, 125-137.
[17] Rajesh Singh, Prabhakar Mishra, Supriya Khare (2019): Estimation of Finite Population Mean Under Measurement Error. Int. J. Comp. Theo. Stat. 6, No. 1, Pp. 63 – 71.
[18] Rajesh Singh, Sakshi Rai (2019): Log-Type Estimators for Estimating Population Mean in Systematic Sampling in the Presence Of Non-Response. Journal of Reliability and Statistical Studies; ISSN (Print): 0974-8024, (Online): 2229-5666, Vol. 12, Issue 1, Pp. 105-115.
[19] Rao P. S. R. S. (1986): Ratio Estimation with Sub-Sampling the Non-Respondents. Survey Methodology, Vol. 12, pp. 217 – 230.
[20] Riaz S., Nazeer A., Abbasi J., Qamar S. (2020): On the Generalized Class of Estimators for Estimation of Finite Population Mean in the Presence of Non-Response Problem. Journal of Prime Research in Mathematics. 16 (1), pp. 52 – 63.
[21] Satici E., Kadilar C. (2011): Ratio Estimator for the Population Mean at the Current Occasion in the Presence of Non-Response in Successive Sampling. Hacettepe J. Math Stat.; 40 (1): pp. 115 – 124.
[22] Singh H, Tailor R. (2003): Use of Known Correlation Coefficient in Estimating the Finite Population Mean. Statistics in Transition, 6 (4): 555 – 560.
[23] Zakir, W. H., Rizvi, S. E. H., Manish, S., and Iqbal, J. B. M. (2021). Efficient Class of Combined Ratio Type Estimator for Estimating the Population Mean under Non-response. International Journal of Scientific Research in Mathematical and Statistical Sciences, 8 (6): Pp. 01-06.
Cite This Article
  • 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

    Copy | Download

    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

    Copy | Download

    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  - 

    Copy | Download

Author Information
  • Department of Statistics, Covenant Polytechnic, Aba, Nigeria

  • Department of Statistics, Federal University of Technology, Owerri, Nigeria

  • Department of Statistics, Federal University of Technology, Owerri, Nigeria

  • Department of Statistics, Federal University of Technology, Owerri, Nigeria

  • Department of Statistics, Abia State University, Uturu, Nigeria

  • Sections