|
An Optimum Stratification For Stratified Cluster Sampling Design When Clusters Are of Varying Sizes
[Full Text]
AUTHOR(S)
Shikha Mehta, V. L. Mandowara
KEYWORDS
Index Terms – Approximate Solutions, Minimal Equations, Optimum Strata Boundaries, SRSWOR, Proportional, Equal and Neyman allocation.
ABSTRACT
Abstract-The paper considers the problem of determining optimum strata boundaries for cluster sampling design considering unequal sizes of clusters. The minimal equations giving optimum strata boundaries by minimising the variance of the estimator of the population mean. sampling in each stratum being carried out independently by simple random sampling without replacement (SRSWOR). These minimal equations are difficult to solve exactly. Thus, the approximate solutions to these minimal equations have been obtained for three allocation methods namely proportional, equal and neyman allocation. The paper concludes with Numerical illustrations.
REFERENCES
[1] Cochran, W.G., “Comparison of methods for determining strata boundaries,” Bull. Inter. Stat. Inst. 38 (2), pp. 345-358 ,1961.
[2] Dalenius, T. and Hodges, J.L., “The choice of stratification points,” Skand.Akt. 40, pp. 198-203,1957.
[3] Dalenius, T., “The problem of optimum stratification-I,” Skand. Akt. 33, pp. 203-13, 1950.
[4] Dalenius, T. and Gurney, M., “The problem of optimum stratification-II,” Skand. Akt. 34, pp.138-48,1951.
[5] Dalenius, T. and Hodges, J.L., “Minimum variance stratification,” JASA, 54, pp. 88-101, 1959.
[6] Ghosh, S.P., “Optimum stratification with two characters,” Ann. Math. Stat. 34, pp. 866-872, 1963.
[7] Gupta, P.C. and Srivastava, N., “Stratification in two staged design,” Paper read before 27th annual conference of the Indian Society of Agri. Stat, 1975.
[8] Gupta, P.C. and Seth, G.R., “On Stratification in sampling involving more than one characters,” Jour. Indian Soc. Ag. Stat. Vol. 31. pp. 1-15, 1979.
[9] Mandowara, V.L. and Gupta, P.C., “Optimum points of stratification for two or more stage design” Communication. In Stat. 23 Issue 3, pp. 947-958, 1994.
[10] Mandowara, V.L. and Gupta, P.C., “Contribution to optimum points of stratification for multi stage designs,” METRON Vol. VII n.1-2, pp. 51-66, 1999.
[11] Mandowara, V.L., “Study of some aspects of the theory of construction of strata,” Ph.D. Thesis, M.L. Sukhadia University, Udaipur (India), 1990.
[12] Mehta Shikha, “Some contributions to construction of strata,” Ph.D. Thesis, M.L. Sukhadia University, Udaipur (India) 2009.
[13] Rajyaguru Arti, “On An Alternative Aspect of Optimum Stratification,”M.Phill Thesis ,South Gujrat University, Surat (India), 1995.
[14] Serfling, R.J., “Approximate optimum stratification,” JASA, 63, pp. 1298-1309, 1968.
[15] Singh, R. and Sukhatme, B.V., “Optimum stratification,” Ann. inst. Stat. Math. 21, pp. 515-528, 1969.
[16] Singh, R., “Determination of optimum strata boundaries,” Jr. Ind. Soc. Ag. Stat. 23, pp. 115-122, 1971.
[17] Singh, R., “On optimum stratification for proportional allocation,” Sankhya, 37, C, Pt. I, pp. 109-115, 1975.
[18] Taga,Y, “On optimum stratification for the objective variable based on concomitant variables using prior information, ” Ann. inst. Stat. Math. 19, pp. 101-130, 1967.
[19] Vinita Singh, “Some contribution to the theory of construction of strata,” Ph.D. Thesis, South Gujrat University, Surat (India), 2005.
|
