ARTICLE
ABSTRACT
The proper choice of strata boundaries is an important factor determining the efficiency of the estimator of the considered characteristics of a population. In this article, the Cum Di(x,z) Rule (i=3,4) for obtaining approximately optimum strata boundaries has been applied, taking into account a single-study variable along with two concomitant variables serving as the basis of the stratification variables. The relative efficiency of the proposed methods has been demonstrated theoretically and empirically by comparing them to a selection of already-existing methods in a simulation study with the use of the proportional allocation method.
KEYWORDS
stratification points, proportional allocation, minimal equation
REFERENCES
Cochran, W. G., (1961).Comparison of methods for determining strata boundaries. Bulletin of the International Statistical Institute, 38, pp. 345–358.
Cochran , W. G., (1963). Sampling Technique. John Wiley and Sons, Inc.
Dalenius, T., (1950). The problem of optimum stratification. Skandinavisk Aktuarietidskrift, 33, pp. 203–213.
Danish, F., Rizvi, S. E .H., (2018). Optimum Stratification in Bivariate Auxiliary Variables under Neyman Allocation. Journal of Modern Applied Statistical Methods, 17(1), 2580. DOI: 10.22237/jmasm/1529418671.
Danish, F., Rizvi, S. E. H., (2019). Optimum Stratification by two Stratifying Variables using Mathematical Programming. Pakistan Journal of Statistics, 35(1), pp. 11–24.
Danish, F., Rizvi, S. E. H., Jeelani, M. I and Reashi, J.A., (2017). Obtaining Strata Boundaries under Proportional Allocation with Varying Cost of Every Unit. Pakistan Journal of Statistics and Operations Research, 13(3), pp. 567–574.
Danish, F., Rizvi, S. E. H., Sharma, M. K. and Jelani, M. I., (2018). Construction of Optimum Strata Boundaries for Uniform and Exponential Auxiliary Variable. Journal of Applied Mathematics & Information Sciences Letters, 6 (1), pp. 37–43.
Danish, F., (2018). A Mathematical Programming approach for obtaining optimum strata boundaries using two auxiliary variables under proportional allocation. Transition in Statistics, 19(3), pp. 507–526. DOI 10.21307/stattrans-2018-028.
Danish, F., Rizvi, S. E. H. and Bouza, C., (2020). On Approximately Optimum Strata Boundaries Using Two Auxiliary Variables. Investigación Operacional, 41 (3), pp. 445–461.
Khan, M. G. M., Nand, N. and Ahmad, N., (2008). Determining the optimum strata boundary points using dynamic programming. Survey Methodology, 34(2), pp. 205–214.
Khan, M. G. M., Prasad, D. K. and Rao, D. K., (2014). On optimum stratification. International Journal of Mathematical, Computational, Natural and Physical Engineering, 8(3), pp. 513–517.
Khan, M. G. M., Reddy, K. G. and D. K. Rao, (2015). Designing stratified sampling in economic and business surveys. Journal of Applied Statistics. DOI: 10.1080/02664763.2015.1018674.
Rizvi, S. E. H., Danish, F., (2018). Construction of Strata Boundaries: A Review. Appl. Math. Inf. Sci. Lett., 6(1), pp. 27–36.
Singh, R., (1975). An alternative method of stratification on the auxiliary variable. Sankhya C, 37, pp. 100–108
Singh, R., Sukhatme, B. V., (1969). Optimum stratification. Annals of Institute of Statistical Mathematics, 21, pp. 515–528.
Yadava, S. S., Singh, R., (1984). Optimum stratification for allocation proportional to strata totals for simple random sampling scheme. Communications in Statistics – Theory and Methods, 13, pp. 2793–2806.
