American Journal of Theoretical and Applied Statistics

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Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response

Received: Dec. 13, 2017    Accepted: Jan. 05, 2018    Published: Feb. 12, 2018
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Abstract

Studies have been carried out on domain mean estimation using non-linear cost function. However little has been done on domain stratum estimation using non-linear cost function using ratio estimation in the presence of non-response. This study develops a method of optimal stratum sample size allocation in domain mean estimation using double sampling with non-linear cost function in the presence of non- response. To obtain an optimum sample size, Lagrangian multiplier technique is employed by minimizing precision at a specified cost. In the estimation of the domain mean, auxiliary variable information in which the study and auxiliary variables both suffers from non-response in the second phase sampling is used. The expressions of the biases and mean square errors of proposed estimator has also been obtained.

DOI 10.11648/j.ajtas.20180702.11
Published in American Journal of Theoretical and Applied Statistics ( Volume 7, Issue 2, March 2018 )
Page(s) 45-57
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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

Optimal Allocation, Double Sampling, Non-Linear Cost Function, Non-Response

References
[1] Cherniyak O. I., (2001). Optimal allocation in stratified sampling and double sampling with non- linear cost function, Journal of Mathematical Sciences 103, 4 pp. 525-528.
[2] Choudhry H. G., Rao, J. N. K, and Michael A., Hidiroglou, (2012). On sample allocation for efficient domain estimation, Survey methodology, 38 (1) pp. 23-29.
[3] Cochran W. G., (1977) Sampling techniques. New York: John Wiley and Sons, (1977).
[4] Eurostat., (2008). Introduction to Sample Design and Estimation Techniques, Survey Sampling Reference Guidelines. Luxembourg; Office for Publication of the European Communities pp. 36.
[5] Hansen M. H. and Hurwitz W. W, (1946). The problem of non-response in sample surveys. The Journal of the American Statistical Association, 41 517-529.
[6] Holmberg A., (2002). A multi-parameter perspective on the choice of sampling designs in surveys. Journal of statistics in transition. 5 (6) pp. 969-994.
[7] Khan S. U., Muhammad Y. S., and Afgan N., (2009). Multi-objective compromise allocation stratified sampling in the presence of non-response using quadratic cost function. International Journal of Business and social science. 5 (13). pp. 162-169.
[8] Neyman, C. and Jerzy D. (1934).; On the Two Different Aspects of the Representative methods of stratified sampling and the method of purposive selection, Journal of royal statistical society. 97 (4) pp. 558-625.
[9] Okafor F. C, (2001). Treatment of non-response in successive sampling, Statistica, 61 (2) 195-204.
[10] Saini M., and Kumar A, (2015). Method of Optimum allocation for Multivariate Stratified two stage Sampling design Using double Sampling. Journal of Probability and Statistics forum, 8, pp. 19-23.
[11] Tschuprow and Al A., (1923). On mathematical expectation of the moments of frequency distribution in the case of correlated observation (chapters 4-6) Metron 2 (1) pp. 646-683, (1923).
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    Alilah David Anekeya, Ouma Christopher Onyango, Nyongesa Kennedy. (2018). Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response. American Journal of Theoretical and Applied Statistics, 7(2), 45-57. https://doi.org/10.11648/j.ajtas.20180702.11

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    ACS Style

    Alilah David Anekeya; Ouma Christopher Onyango; Nyongesa Kennedy. Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response. Am. J. Theor. Appl. Stat. 2018, 7(2), 45-57. doi: 10.11648/j.ajtas.20180702.11

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    AMA Style

    Alilah David Anekeya, Ouma Christopher Onyango, Nyongesa Kennedy. Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response. Am J Theor Appl Stat. 2018;7(2):45-57. doi: 10.11648/j.ajtas.20180702.11

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  • @article{10.11648/j.ajtas.20180702.11,
      author = {Alilah David Anekeya and Ouma Christopher Onyango and Nyongesa Kennedy},
      title = {Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {7},
      number = {2},
      pages = {45-57},
      doi = {10.11648/j.ajtas.20180702.11},
      url = {https://doi.org/10.11648/j.ajtas.20180702.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20180702.11},
      abstract = {Studies have been carried out on domain mean estimation using non-linear cost function. However little has been done on domain stratum estimation using non-linear cost function using ratio estimation in the presence of non-response. This study develops a method of optimal stratum sample size allocation in domain mean estimation using double sampling with non-linear cost function in the presence of non- response. To obtain an optimum sample size, Lagrangian multiplier technique is employed by minimizing precision at a specified cost. In the estimation of the domain mean, auxiliary variable information in which the study and auxiliary variables both suffers from non-response in the second phase sampling is used. The expressions of the biases and mean square errors of proposed estimator has also been obtained.},
     year = {2018}
    }
    

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    AB  - Studies have been carried out on domain mean estimation using non-linear cost function. However little has been done on domain stratum estimation using non-linear cost function using ratio estimation in the presence of non-response. This study develops a method of optimal stratum sample size allocation in domain mean estimation using double sampling with non-linear cost function in the presence of non- response. To obtain an optimum sample size, Lagrangian multiplier technique is employed by minimizing precision at a specified cost. In the estimation of the domain mean, auxiliary variable information in which the study and auxiliary variables both suffers from non-response in the second phase sampling is used. The expressions of the biases and mean square errors of proposed estimator has also been obtained.
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Author Information
  • Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya

  • Departments of Statistics and Actuarial Science, Kenyatta University, Nairobi, Kenya

  • Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya

  • Section