Compromise Allocation for Combined Ratio Estimates of Population Means of a Multivariate Stratified Population Using Double Sampling in Presence of Non-Response

This paper is an attempt to work out a compromise allocation to construct combined ratio estimates under multivariate double sampling design in presence of non-response when the population mean of the auxiliary variable is unknown. The problem has been formulated as a multi-objective integer non-linear programming problem. Two solution procedures are developed using goal programming and fuzzy programming techniques. A numerical example is also worked out to illustrate the computational details. A comparison of the two methods is also carried out.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Iftekhar, S. , Ali, Q. and Ahsan, M. (2014) Compromise Allocation for Combined Ratio Estimates of Population Means of a Multivariate Stratified Population Using Double Sampling in Presence of Non-Response. Open Journal of Optimization, 3, 68-78. doi: 10.4236/ojop.2014.34007.

 [1] Hansen, M.H. and Hurwitz, W.N. (1946) The Problem of Non-Response in Sample Surveys. Journal of the American Statistical Association, 41, 517-529. http://dx.doi.org/10.1080/01621459.1946.10501894 [2] Rao, P.S.R.S. (1986) Ratio Estimation with Sub-Sampling the Non-Respondents. Survey Methodology, 12, 217-230. [3] Rao, P.S.R.S. (1987) Ratio and Regression Estimates with Sub-Sampling the Non-Respondents. Special Contributed Session of the International Statistical Association Meeting, 2-16 September 1987, Tokyo. [4] Khare, B.B. and Srivastva, S. (1993) Estimation of Population Mean Using Auxiliary Character in Presence of NonResponse. National Academy Science Letters, 16, 111-114. [5] Khare, B.B. and Srivastva, S. (1997) Transformed Ratio Type Estimators for the Population Mean in the Presence of Non-Response. Communications in Statistics—Theory and Methods, 26, 1779-1791. http://dx.doi.org/10.1080/03610929708832012 [6] Raiffa, H. and Schlaifer, R. (1961) Applied Statistical Decision Theory. Graduate School of Business Administration, Harvard University, Boston. [7] Ericson, W.A. (1965) Optimum Stratified Sampling Using Prior Information. Journal of the American Statistical Association, 60, 750-771. http://dx.doi.org/10.1080/01621459.1965.10480825 [8] Ahsan, M.J. and Khan, S.U. (1982) Optimum Allocation in Multivariate Stratified Random Sampling with Overhead Cost. Metrika, 29, 71-78. http://dx.doi.org/10.1007/BF01893366 [9] Dayal, S. (1985) Allocation in Sample Using Values of Auxiliary Characteristics. Journal of Statistical Planning and Inference, 11, 321-328. http://dx.doi.org/10.1016/0378-3758(85)90037-0 [10] Khan, M.G.M., Maiti, T. and Ahsan, M.J. (2010) An Optimal Multivariate Stratified Sampling Design Using Auxiliary Information: An Integer Solution Using Goal Programming Approach. Journal of Official Statistics, 26, 695-708. [11] Varshney, R., Najmussehar and Ahsan, M.J. (2011) An Optimum Multivariate Stratified Double Sampling Design in Non-Response. Optimization Letters, 6, 993-1008. [12] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley& Sons, New York. [13] Schniederjans, M.J. (1995) Goal Programming: Methodology and Applications. Kluwer, Dordrecht. http://dx.doi.org/10.1007/978-1-4615-2229-4 [14] Lingo User’s Guide (2013) Lingo-User’s Guide. LINDO SYSTEM INC., Chicago. [15] Haseen, S., Iftekhar, S., Ahsan, M.J. and Bari, A. (2012) A Fuzzy Approach for Solving Double Sampling Design in Presence of Non-Response. International Journal of Engineering Science and Technology, 4, 2542-2551. [16] Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. and Asok, C. (1984) Sampling Theory of Surveys with Applications. 3rd Edition, Iowa State University Press, Iowa and Indian Society of Agricultural Statistics, New Delhi.