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

Alilah David Anekeya; Ouma Christopher Onyango; Nyongesa Kennedy

doi:doi:10.11648/j.ajtas.20180702.11

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

Alilah David Anekeya, Ouma Christopher Onyango, Nyongesa Kennedy

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 2)

Received: 13 December 2017 Accepted: 5 January 2018 Published: 12 February 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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 2)
DOI	10.11648/j.ajtas.20180702.11
Page(s)	45-57
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), 2018. 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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response
AU  - Alilah David Anekeya
AU  - Ouma Christopher Onyango
AU  - Nyongesa Kennedy
Y1  - 2018/02/12
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180702.11
DO  - 10.11648/j.ajtas.20180702.11
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  - 45
EP  - 57
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180702.11
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.
VL  - 7
IS  - 2
ER  -

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Author Information

Alilah David Anekeya

Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya
Ouma Christopher Onyango

Departments of Statistics and Actuarial Science, Kenyatta University, Nairobi, Kenya
Nyongesa Kennedy

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

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APA Style

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Optimal Allocation in Domains Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non-Response
AU  - Alilah David Anekeya
AU  - Ouma Christopher Onyango
AU  - Nyongesa Kennedy
Y1  - 2018/02/12
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180702.11
DO  - 10.11648/j.ajtas.20180702.11
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  - 45
EP  - 57
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180702.11
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.
VL  - 7
IS  - 2
ER  -

Copy | Download