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On the Coverage Properties of the Ratio Based Estimator in Presence of Non Response Error

Received: 23 April 2022     Accepted: 7 May 2022     Published: 19 May 2022
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Abstract

Sample surveys are taken with the assumption that all the sampled elements will respond. However, this is not always the case. Sometimes missing values occur in the survey data due to some reasons. In cases of such missing values, any inference from the data will survey from a non-response error. Therefore, the researcher needed to put all measures in place to prevent the occurrence of the missing values in the data. However, this is not easily achieved. The non-response may occur even after all measures to prevent it have been put in place. Therefore, there is a need to correct the error if it so happens. The current paper seeks to improve the Hansel and Hurwitz (1946) estimator using poststratification. The proposed estimator can be as well be improved. Therefore, the current study proposes an improvement of the Hansel and Hurwitz (1946) estimator using the median of the auxiliary variable. The efficiency of the new proposed estimator is checked using the confidence interval length. Which is the on-coverage property of the estimator. On to the recommendation a band with that will reduce the variance in case of high non-response rate is thus suggested for further studies. Beside we suggest further studies on how both variances and bias will be minimized without any of them being minimized in expense of the other.

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 3)
DOI 10.11648/j.ajtas.20221103.12
Page(s) 89-93
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

Confidence Interval, Variance, No-Response, Mean

References
[1] Calonico, S. C. (2018). Coverage error optimal confidence intervals for local polynomial regression. arXiv preprint arXiv: 1808.01398.
[2] Calonico, S. C. (2018). On the effect of bias estimation on coverage accuracy in nonparametric inference. pp. 113 (522), 767-779.
[3] Calonico, S. C. (2020). Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs.. The Econometrics Journal, 23 (2), 192-210.
[4] Frank, B. &. (2021). Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation. Forests, 12 (6), 772.
[5] Gardasevic, J. (2019). Standing Height and its Estimation Utilizing Tibia Length Measurements in Adolescents from Western Region in Kosovo. International Journal of Morphology, 37 (1).
[6] Gardasevic, J. M. (2019). RELATIONSHIP BETWEEN TIBIA LENGTH MEASUREMENTS AND STANDING HEIGHT.. Anthropologie, (1962-), 57 (3), 263-270.
[7] Goulet-Pelletier, J. C. (2018). A review of effect sizes and their confidence intervals, Part I: The Cohen's family.. The Quantitative Methods for Psychology, 14 (4), 242-265.
[8] Hartley, H. O. (2019). A new estimation theory for sample surveys. Biometrika, 55 (3), 547-557.
[9] Herbert, I. O. (2018). Incorporation Of The Jackknifing Procedure Into The Three-Stage Cluster Sampling Design In The Estimation Of Finite Population Totals.
[10] Lee, D. S. (2021). Valid t-ratio Inference for IV (No. w29124). National Bureau of Economic Research.
[11] Nayak, M. S. (2019). "Strengths and weaknesses of online surveys.". technology, 6 (2019): 7.
[12] Nderitu, C. W. (2022). Estimation of Finite Population Mean Using Ratio Estimator Based on Known Median of Auxiliary Variable in the Presence of Non-Response.. American Journal of Theoretical and Applied Statistics, 11 (2), 75-82.
[13] Singh, G. N. (2021). Enhanced estimation of the population distribution function in the presence of non-response. Ain Shams Engineering Journal, 12 (3), 3109-3119.
[14] Singh, P. S. (2018). Effect of measurement error and non-response on the estimation of the population mean.. Investigación Operacional, 39 (1), 108-120.
[15] Singh, R. K. (2009). Estimation of mean in presence of non-response using an exponential estimator. Infinite Study.
[16] Yang, L. D. (2020). Estimation of incubation period and serial interval of COVID-19: analysis of 178 cases and 131 transmission chains in Hubei province, China.. Epidemiology & Infection, 148.
Cite This Article
  • APA Style

    Charles Wanyingi Nderitu, Herbert Imboga, Samuel Mwangi Gathuka. (2022). On the Coverage Properties of the Ratio Based Estimator in Presence of Non Response Error. American Journal of Theoretical and Applied Statistics, 11(3), 89-93. https://doi.org/10.11648/j.ajtas.20221103.12

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    ACS Style

    Charles Wanyingi Nderitu; Herbert Imboga; Samuel Mwangi Gathuka. On the Coverage Properties of the Ratio Based Estimator in Presence of Non Response Error. Am. J. Theor. Appl. Stat. 2022, 11(3), 89-93. doi: 10.11648/j.ajtas.20221103.12

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    AMA Style

    Charles Wanyingi Nderitu, Herbert Imboga, Samuel Mwangi Gathuka. On the Coverage Properties of the Ratio Based Estimator in Presence of Non Response Error. Am J Theor Appl Stat. 2022;11(3):89-93. doi: 10.11648/j.ajtas.20221103.12

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  • @article{10.11648/j.ajtas.20221103.12,
      author = {Charles Wanyingi Nderitu and Herbert Imboga and Samuel Mwangi Gathuka},
      title = {On the Coverage Properties of the Ratio Based Estimator in Presence of Non Response Error},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {11},
      number = {3},
      pages = {89-93},
      doi = {10.11648/j.ajtas.20221103.12},
      url = {https://doi.org/10.11648/j.ajtas.20221103.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221103.12},
      abstract = {Sample surveys are taken with the assumption that all the sampled elements will respond. However, this is not always the case. Sometimes missing values occur in the survey data due to some reasons. In cases of such missing values, any inference from the data will survey from a non-response error. Therefore, the researcher needed to put all measures in place to prevent the occurrence of the missing values in the data. However, this is not easily achieved. The non-response may occur even after all measures to prevent it have been put in place. Therefore, there is a need to correct the error if it so happens. The current paper seeks to improve the Hansel and Hurwitz (1946) estimator using poststratification. The proposed estimator can be as well be improved. Therefore, the current study proposes an improvement of the Hansel and Hurwitz (1946) estimator using the median of the auxiliary variable. The efficiency of the new proposed estimator is checked using the confidence interval length. Which is the on-coverage property of the estimator. On to the recommendation a band with that will reduce the variance in case of high non-response rate is thus suggested for further studies. Beside we suggest further studies on how both variances and bias will be minimized without any of them being minimized in expense of the other.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - On the Coverage Properties of the Ratio Based Estimator in Presence of Non Response Error
    AU  - Charles Wanyingi Nderitu
    AU  - Herbert Imboga
    AU  - Samuel Mwangi Gathuka
    Y1  - 2022/05/19
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ajtas.20221103.12
    DO  - 10.11648/j.ajtas.20221103.12
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 89
    EP  - 93
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20221103.12
    AB  - Sample surveys are taken with the assumption that all the sampled elements will respond. However, this is not always the case. Sometimes missing values occur in the survey data due to some reasons. In cases of such missing values, any inference from the data will survey from a non-response error. Therefore, the researcher needed to put all measures in place to prevent the occurrence of the missing values in the data. However, this is not easily achieved. The non-response may occur even after all measures to prevent it have been put in place. Therefore, there is a need to correct the error if it so happens. The current paper seeks to improve the Hansel and Hurwitz (1946) estimator using poststratification. The proposed estimator can be as well be improved. Therefore, the current study proposes an improvement of the Hansel and Hurwitz (1946) estimator using the median of the auxiliary variable. The efficiency of the new proposed estimator is checked using the confidence interval length. Which is the on-coverage property of the estimator. On to the recommendation a band with that will reduce the variance in case of high non-response rate is thus suggested for further studies. Beside we suggest further studies on how both variances and bias will be minimized without any of them being minimized in expense of the other.
    VL  - 11
    IS  - 3
    ER  - 

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Author Information
  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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