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
Volume 7, Issue 2, March 2018, Pages: 45-57
Received: Dec. 13, 2017;
Accepted: Jan. 5, 2018;
Published: Feb. 12, 2018
Views 789 Downloads 37
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
Follow on us
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.
Optimal Allocation, Double Sampling, Non-Linear Cost Function, Non-Response
To cite this article
Alilah David Anekeya,
Ouma Christopher Onyango,
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.
Vol. 7, No. 2,
2018, pp. 45-57.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
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.
Cochran W. G., (1977) Sampling techniques. New York: John Wiley and Sons, (1977).
Eurostat., (2008). Introduction to Sample Design and Estimation Techniques, Survey Sampling Reference Guidelines. Luxembourg; Office for Publication of the European Communities pp. 36.
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.
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.
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.
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.
Okafor F. C, (2001). Treatment of non-response in successive sampling, Statistica, 61 (2) 195-204.
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.
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).