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Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling

Received: 17 September 2017     Accepted: 4 October 2017     Published: 10 November 2017
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Abstract

The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)
DOI 10.11648/j.ajtas.20170606.12
Page(s) 270-277
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), 2017. Published by Science Publishing Group

Keywords

Finite Population with Linear Trend, Systematic Sampling, Measurement Errors

References
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[8] Plankey, M., Stevens, J., Flegal, K., and Rust, P. (1997). Prediction equations do not eliminate systematic error in self-reported body mass index. Obesity Research, 5(4):308-314.
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[17] O’ Neil, D. and Olive, S. (2013). The consequences of measurment error when estimating the impact of obesity on income. IZA Journal of Labor Economics, 2(3).
[18] Subramani, J. and Singh, S. (2014). Estimation of population mean in the presence of linear trend. Communications in the Statistics-Theory and Methods, 43.
[19] Ouko, A., Cheruiyot, W., and Emily, K. (2014). Effects of measurement errors on population estimates from samples generated from a stratified population through systematic sampling technique. Expert Journal of Economics, 2:120-132.
[20] Grellety, E. Golden, M. H (2016). The effect of Random error on diagnosis accuracy illustrated with the anthropometric diagnosis of malnutrition. PLoS ONE 11(12): e0168585 doi 10.1371.
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Cite This Article
  • APA Style

    Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick. (2017). Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. American Journal of Theoretical and Applied Statistics, 6(6), 270-277. https://doi.org/10.11648/j.ajtas.20170606.12

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    ACS Style

    Oloo Odhiambo Erick; James Kahiri; Wafula Mike Erick. Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. Am. J. Theor. Appl. Stat. 2017, 6(6), 270-277. doi: 10.11648/j.ajtas.20170606.12

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    AMA Style

    Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick. Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. Am J Theor Appl Stat. 2017;6(6):270-277. doi: 10.11648/j.ajtas.20170606.12

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  • @article{10.11648/j.ajtas.20170606.12,
      author = {Oloo Odhiambo Erick and James Kahiri and Wafula Mike Erick},
      title = {Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {6},
      pages = {270-277},
      doi = {10.11648/j.ajtas.20170606.12},
      url = {https://doi.org/10.11648/j.ajtas.20170606.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.12},
      abstract = {The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.},
     year = {2017}
    }
    

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    AU  - Oloo Odhiambo Erick
    AU  - James Kahiri
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    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    AB  - The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.
    VL  - 6
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Author Information
  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

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