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On Optimum Stratification Using Mathematical Programming Approach
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Optimum stratification is a technique which results in minimum possible variance of the estimator for the population characteristic under study. The main objective of stratification is to give a better cross-section of the population so as to gain a higher degree of relative precision. The problem of determining optimum strata boundaries (OSB) was pioneered by Dalenius (1950). The problem of obtaining OSB was recently studied by Khan et al. (2009) who formulated the problem as a mathematical programming problem (MPP) by minimizing variance of the estimated population parameter subject to the condition that the sum of the widths of all the strata would be equal to the range of the given distribution under given allocation procedure. In the present investigation the problem of finding OSB has been taken into consideration as the problem of optimum strata width (OSW), using MPP by dynamic programming technique, when the study variable is uniformly distributed. Empirical study has also been taken where it is revealed that with the increase in the number of strata to a fixed number the precision of the method goes on increasing. Also the proposed method proves better than other stratification method (Singh, 1967).
Keywords
Mathematical Programming Problem, Optimum Stratification, Optimum Strata Boundaries, Optimum Strata Width.
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- Aoyama, H. (1954). A study of stratified random sampling. Annl. Instit. Statist. Mathemat., 6 : 1-36.
- Cochran, W.G. (1977). Sampling techniques. 3rd Ed. John Wiley and Sons, Inc., NEW YORK, U.S.A.
- Dalenius, T. (1950). The problem of optimum stratification. Skandinavisk Aktuarietidskrift, 33 : 203-213.
- Dalenius, T. and Gurney, M. (1951). The problem of optimum stratification II. Skandinavisk Aktuarietidskrift, 34 : 133-148.
- Dalenius, T. and Hodges, J.L. Jr. (1959). Minimum variance stratification. J. American Statist. Assoc., 54 : 88-101.
- Ekman, G. (1959). Approximation expression for the conditional mean and variance over small intervals of a continuous distribution. Annl. Mathemat. Statist., 30 : 1131-1134.
- Gupta, R. K., Singh, R. and Mahajan, P. K. (2005).Approximate optimum strata boundaries for ratio and regression estimators. Aligarh J. Statist., 25 : 49-55.
- Hidiroglou, M.A. and Srinath, K.P. (1993). Problems associated to sub annual business surveys. J. Business & Econ. Statist., 11 : 397-405.
- Isii, K. and Taga, Y. (1969). On optimal stratification for multivariate distributions. Skand. Akt., 52 : 24-38.
- Khan, E. A. Khan, M. G. M. and Ahsan, M. J. (2002).Optimum stratification:A mathematical programming approach. Calcutta Statist. Assoc. Bull., 52 : 323-333.
- Khan, M.G.M., Ahmad, N. and Khan, S. (2009). Determination the optimum stratum boundaries using mathematical programming. J. Mathemat. Modelling & Algorithms, 8 : 409-423.
- Kozak, M. and Verma, M.R. (2006). Geometric versus optimization stratification: A comparison of efficiency. Survey Methodology, 32(2) : 157-163.
- Lavallee, P. and Hidiriglou, M. (1988). On the stratification of skewed populations. Survey Methodology, 14 : 33-43.
- Mahalanobis, P.C. (1952). Some aspect of design of sample surveys. Sankhya, 12 : 1-17.
- Rivest, R.J. (2002). A generalization of Lavallee and Hidiroglou algorithm for stratification in survey. Survey Methodology, 28 : 191-198.
- Rizvi, S.E.H., Gupta, J.P and Bargava, M. (2002). Optimum stratification based on auxiliary variable for compromise allocation.Metron, 28 (1) : 201-215.
- Serfling, R.J. (1968). Approximately optimum stratification. J. American Statist. Assoc., 63 : 1298-1309.
- Singh, R. (1967). Some contributions to the theory of construction of Strata. Ph.D. Thesis, Indian Agriculture Research Institute, NEW DELHI, INDIA.
- Singh, R. (1971). Approximately optimum stratification on auxiliary variable. J. American Statist. Assoc., 66 : 829-833.
- Sweet, E.M. and Sigman, R.S. (1995).Evaluation of model-assisted procedures for stratifying skewed populations using auxiliary data. Proceedings of the Survey Research Methods Section, American Statistical Association, Alexandria, 491–496.
- Unnithan, V.K.G. (1978). The minimum variance boundary points of stratification. Sankhya, 40 (C) : 60-72.
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