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On Optimum Stratification

Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

Abstract:

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: dynamic programming technique, auxiliary variable, nonlinear programming problem, optimum stratification, uniform distribution

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091262

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References:


[1] Aoyama, H. (1954). A Study of Stratified Random Sampling. Ann. Inst. Stat. Math., 6, 1-36.
[2] Bellman, R.E. (1957). Dynamic Programming .Princetown University Press, New Jersey.
[3] Dalenius, T. (1950). The Problem of Optimum Stratification-II. Skand. Aktuartidskr, 33, 203-213.
[4] Dalenius, T. (1957). Sampling in Sweden. Almqvist & Wiksell, Stockholm.
[5] Dalenius, T. and Gurney, M. (1951). The Problem of Optimum stratification-II, Skand.Akt., 34, 133-148.
[6] Dalenius, T. and Hodges, J. L. (1959): Minimum Variance Stratification. J. Amer. Statist. Assoc. 54, 88-101.
[7] Durbin, J. (1959): Review of Sampling in Sweden. J. Roy. Statist. Soc. (A) 122, 146-148.
[8] Gupta, R. K., Singh, R. and Mahajan, P. K. (2005). Approximate Opimumum Strata Boundaries for Ratio and Regression Estimators. Aligarh Journal of Statistics, 25, 49-55.
[9] Hansen, M. H., Hurwitz, W. N. and Madow, W. G. (1953): Sample Survey Methods and Theory. Vol. I & II, John Wiley and Sons, Inc., New York.
[10] Khan, M. G. M., Ahmad, N. and Khan, Sabiha (2009). Determining the Optimum Stratum Boundaries using Mathematical Programming. Journal of Mathematical Modelling and Algorithms", Springer, Netherland, DOI 10.1007/s10852-009-9115-3, 8(4), 409-423.
[11] Khan, E. A., Khan, M. G. M. and Ahsan, M. J. (2002). Optimum Stratification: A Mathematical Programming Approach, Calcutta Statistical Association Bulletin, 52 (special Volume), 323-333.
[12] Khan, M. G. M., Najmussehar and Ahsan, M. J. (2005). Optimum Stratification for Exponential Study Variable under Neyman Allocation. Journal of Indian Society of Agricultural Statistics, 59(2), 146-150.
[13] Khan, M. G. M., Nand, N. and Ahmad, N. (2008). Determining the Optimum Strata Boundary Points Using Dynamic Programming. Survey Methodology, 34(2), 205-214.
[14] Khan, M.G.M.; Rao, D.; Ansari, A.H. and Ahsan, M.J. (2013). Determining Optimum Strata Boundaries and Sample Sizes for Skewed Population with Log-normal Distribution. Journal of Communications in Statistics - Simulation and Computation. (To appear).
[15] Mahalanobis, P. C. (1952). Some Aspects of the Design of Sample Surveys. Sankhya, 12, 1-7.
[16] Mehta, S. K., Singh, R. and Kishore, L. (1996). On Optimum Stratification for Allocation Proportional to Strata Totals. Journal of Indian Statistical Association, 34, 9-19.
[17] Murthy, M. N. (1967). Sampling Theory and Methods. Statistical Publishing Society, Calcutta.
[18] Neyman, J. (1934). On the Two Different Aspects of the Representatives Methods: the Method Stratified Sampling and the Method of Purposive Selection. J. Roy. Stat. Soc. 97, 558-606.
[19] Rizvi, S. E. H., Gupta, J. P. and Bhargava, M. (2002). Optimum Stratification based on Auxiliary Variable for Compromise Allocation. Metron, 28(1), 201-215.
[20] Sethi, V. K. (1963). A Note on Optimum Stratification of Population for Estimating the Population Mean. Aust. J. Statist., 5, 20-33.
[21] Singh, R. and Parkash, D. (1975). Optimum Stratification for Equal Allocation. Annals of the Institute of Statistical Mathematics, 27, 273-280.
[22] Singh, R. (1971). Approximately Optimum Stratification on the Auxiliary Variable. J. Amer. Stat. Assc., 66, 829-833.
[23] Singh, R. (1975). An Alternate Method of Stratification on the Auxiliary Variable. Sankhya. C, 37, 100-108.
[24] Singh, R. and Sukhatme, B. V. (1969). Optimum Stratification for Equal Allocation. Ann. Inst. Stat. Math., 27, 273-280.
[25] Singh, R. and Sukhatme, B. V. (1972). Optimum Stratification in Sampling with Varying Probabilities. Ann. Inst. Stat. Math., 24, 485-494.
[26] Singh, R. and Sukhatme, B. V. (1973). Optimum Stratification with Ratio and Regression Methods of Estimation. Annals of the Institute of Statistical Mathematics, 25, 627-633.
[27] Taha, H. A. (2007), Operations Research: An Introduction, 8th edition, Pearson Education, Inc., New Jersey.
[28] Taga, Y. (1967). On Optimum Stratification for the Objective Variable Based on Concomitant Variables using Prior Information. Annals of the Institute of Statistical Mathematics, 19, 101-129.
[29] Wackerly, D.W., Mendenhall, W. and Scheaffer, R. (2008). Mathematical Statistics with Applications (8thEddition), Thomson Learning, Inc., USA.