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

Received: 17 December 2017     Accepted: 5 January 2018     Published: 15 February 2018
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Abstract

This paper describes theoretical estimation of domains mean using double sampling with a non-linear cost function in the presence of non-response. The estimation of domain mean is proposed using auxiliary information in which the study and auxiliary variable suffers from non-response in the second phase sampling. The expression of the biases and mean square errors of the proposed estimators are obtained. The optimal stratum sample sizes for given set of non-linear cost function are developed.

Published in Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 1)
DOI 10.11648/j.sjams.20180601.14
Page(s) 28-42
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

Double Sampling for Ratio Estimation, Domain Mean, Auxiliary Variable, Non-Linear Cost Function and Non-Response

References
[1] Aditya, K., Sud U., and Chandra H., (2014). Estimation of Domain Mean Using Two-Stage Sampling with Sub-Sampling Non-response. Journal of the Indian Society of Agricultural Statistics 68 (1) pp. 39-54.
[2] Cochran W. G., (1977) Sampling techniques. New York: John Wiley and Sons, (1977).
[3] Chaudhary M. K, and Kumar A., (2016). Estimation of Mean of Finite Population using Double sampling Scheme under Non-response, Journal of Mathematical Sciences 5 (2), 4 pp 287 297.
[4] Gamrot, W., (2006). Estimation of Domain Total under Non-response using Double Sampling, Statistics in Transition, 7 (4) pp. 831-840.
[5] Hansen M. H. and Hurwirtz W. W, (1946). The problem of Non-response in Sample Surveys, The Journal of the American Statistical Association, 41 517-529.
[6] Kalton, G., and Kasprzyk, D (1986). The treatment of Missing Survey Data, Survey Methodology, 12 pp. 1-16.
[7] Meeden, G., (2005). A Non-information Bayesian Approach to Domain Estimation. Journal of Statistical Planning and Inference, 129 (2) pp. 85-92.
[8] Oh, H. L, and Scheuren F. J., (1983). Weighting adjustments for unit non-response, In W. G Madow, I, Olkin And B Rudin (Eds), Incomplete data in sample surveys New, York Academic press, 2 pp 143-184.
[9] Okafor F. C, (2001). Treatment of Non-response in Successive Sampling, Statistica, 61 (2) 195 204.
[10] Sahoo, L. N and Panda, P., (199). Estimation Using Auxiliary Information in Two-Stage Sampling, Austrialian and New Zealand Journal of Statistics 41 (4) pp. 405-410.
[11] Srivastava, S. K., Jhajj, H. S., (1983). A Class of Estimators of Population Means Using Multi-Auxiliary Information. Cal. Stat. Assoc. Bull. 10 (2) pp. 47-56.
[12] Udofia G. A., (2002). Estimation for Domains in Double Sampling for Probabilities Proportional to Size, the Indian Journal of Statistics 63 pp. 82-89.
Cite This Article
  • APA Style

    Alila David Anekeya, Ouma Christopher Onyango, Nyongesa Kennedy. (2018). Domain Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non Response. Science Journal of Applied Mathematics and Statistics, 6(1), 28-42. https://doi.org/10.11648/j.sjams.20180601.14

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    ACS Style

    Alila David Anekeya; Ouma Christopher Onyango; Nyongesa Kennedy. Domain Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non Response. Sci. J. Appl. Math. Stat. 2018, 6(1), 28-42. doi: 10.11648/j.sjams.20180601.14

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    AMA Style

    Alila David Anekeya, Ouma Christopher Onyango, Nyongesa Kennedy. Domain Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non Response. Sci J Appl Math Stat. 2018;6(1):28-42. doi: 10.11648/j.sjams.20180601.14

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  • @article{10.11648/j.sjams.20180601.14,
      author = {Alila David Anekeya and Ouma Christopher Onyango and Nyongesa Kennedy},
      title = {Domain Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non Response},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {6},
      number = {1},
      pages = {28-42},
      doi = {10.11648/j.sjams.20180601.14},
      url = {https://doi.org/10.11648/j.sjams.20180601.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20180601.14},
      abstract = {This paper describes theoretical estimation of domains mean using double sampling with a non-linear cost function in the presence of non-response. The estimation of domain mean is proposed using auxiliary information in which the study and auxiliary variable suffers from non-response in the second phase sampling. The expression of the biases and mean square errors of the proposed estimators are obtained. The optimal stratum sample sizes for given set of non-linear cost function are developed.},
     year = {2018}
    }
    

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    T1  - Domain Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non Response
    AU  - Alila David Anekeya
    AU  - Ouma Christopher Onyango
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    T2  - Science Journal of Applied Mathematics and Statistics
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    JO  - Science Journal of Applied Mathematics and Statistics
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    AB  - This paper describes theoretical estimation of domains mean using double sampling with a non-linear cost function in the presence of non-response. The estimation of domain mean is proposed using auxiliary information in which the study and auxiliary variable suffers from non-response in the second phase sampling. The expression of the biases and mean square errors of the proposed estimators are obtained. The optimal stratum sample sizes for given set of non-linear cost function are developed.
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Author Information
  • Department of Mathematics Masinde Muliro University of Science and Technology, Kakamega, Kenya

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

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

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