Oriental Journal of Computer Science and Technology

Open Access Open Access  Restricted Access Subscription Access

Optimal Allocation of Stratified Sampling Design Using Gradient Projection Method


Affiliations
1 Division of Agri.stat, SKUAST-K, Kashmir, India
 

This article deals with the problem of finding an optimal allocation of sample sizes in stratified sampling design to minimize the cost function. In this paper the iterative procedure of Rosen’s Gradient projection method is used to solve the Non linear programming problem (NLPP), when a non integer solution is obtained after solving the NLPP then Branch and Bound method provides an integer solution.

Keywords

Stratification, Optimal Allocation, Nonlinear Programming, Gradient Projection Method, Branch and Bound Method and Integer Allocation.
User
Notifications
Font Size

  • Ahsan, M. J., Najmussehar and Khan ,M. G.M. Mixed allocation in stratified sampling.Aligrah Journal of Statistics sciences 25,87-97, (2005).

  • Ansari A.H., Najmussehar and Ahsan M.J. On Multiple Response Stratified Random Sampling Design, International Journal of Statistical Sciences, 1, 45-54, (2009).

  • Aoyama H. Stratified Random Sampling with Optimum Allocation for Multivariate Populations, Annals of the institute of statistical Mathematics. 14, 251–258, (1963).

  • Arthanari ,T.S., and Dodge, Y. Mathematical programming in statistics. New York: John Willy (1981).

  • Bethel J. Sample Allocation in Multivariate Surveys. Survey Methodology, 15, 40-57, (1989) .

  • Chatterjee, S. A study of optimum allocation in multivariate stratified surveys. Skandinavisk Actuarietidskrift 55,73-80, (1972).

  • Chatterjee, S. Multivariate stratified surveys. Journal of American statistics Association. 63,530-535, (1968).

  • Chromy, J. R. Design Optimization with Multiple Objectives. In: Proceedings of the Survey Research Methods section. Alexandria, VA: American Statistical Association, (1987)194–199 .

  • Cochran W.G. Sampling Techniques, 3rd edition. John Wileyand Sons, New York (1977).

  • Dalenius. Sampling in Sweden. Contributions to the Methods and Theories of Sample Survey Practice. Stockholm: Almqvist and Wicksell (1957).

  • Folks, J.K., Antle, C.E. Optimum allocation of samplingunits to the strata when there are R responses of interest. Journal of American Statistical Association 60, 225-233, (1965).

  • Ghosh,S.P. A note on stratified random sampling with multiple characters. Calcutta Statistical Bulletin 8, 81-89, (1958).

  • Gren , J. Some Application of Non-linear Programming in Sampling Methods, Przeglad Statystyczny, 13,203–217, (1966) (in Polish).

  • Hartley H.O. Multiple purpose optimum allocation in stratified sampling, in : Proceedings of the American Statistical Association, Social Statistics Section. Alexandria, VA: American Statistical Association, (1965) 258-261.

  • Khan. M.G.M., and Ahsan, M. J., and Jahan, N. An optimal multivariate stratified sampling using dynamic programming .Australian & New Zealand of statistics 45, 107-113, (2003).

  • Khan. M.G.M., and Ahsan, M. J., and Jahan, N. Compromise allocation in multivariate stratified sampling : An integer solution. Naval Research Logistics 44, 69-79, (1997).

  • Kokan, A. R. and Khan, S. U. Optimum allocation in multivariate surveys: An analytical solution. Journal of Royal Statistical Society, Ser. B, 29, 115-125, (1967).

  • Kozok M. On sample allocation in multivariate surveys, Communication in Statistics-Simulation and Computation, 35, 901-910, (2006).

  • Kreienbrock, L . Generalized measures of dispersion to solve the allocation problem in multivariate stratified random sampling. Communication in Statistics : theory and methods 22, 219-239, (1993).

  • Lingo 13.0, LINDO inc.ltd.

  • Mohd.Vaseem Ismail et al. Multi-objective convex programming problem arising in multivariate sampling. International Journal of Engineering Science and Technology 2, 291-296, (2010).

  • Neyman, J. On the two Different aspects of the representative method: The method of stratified sampling and the method of purposive selection. Journal of Royal Statistical Society 97, 558-625, (1934).

  • P. V. Sukhatme, B. V. Sukhatme, Sukhatme, C. Asok. Sampling theory of Surveys with Applications. Iowa State University Press, Iowa, U. S. A. and Indian Society of Agricultural Statistics, New Delhi, India (1984).

  • Rosen, J.B. The gradient projection method For Nonlinear Programming, Part i, linear constraints. SIAM journal of Applied Mathematics 8, 181-219, (1960).

  • Rosen, J.B. The gradient projection method For Nonlinear Programming, Part ii, Nonlinear constraints. SIAM journal of Applied Mathematics 9, 514-553, (1961).

  • Thompson, M.E. Theory of Sample Surveys. Chapman & Hall (1997).

  • Wywial J. Minimizing the Spectral Radius of Means Vector from Sample Variance–covariance Matrix Sample Allocation between Strata, Prace Naukowe Akademii Ekonomicznej we Wroclawiu. Wroclaw, Poland, 404, 223–235, (1988) (in Polish).

  • Yates, F. Sampling Methods for Censuses and Surveys. 3rd ed. London: Charles Griffin (1960).


Abstract Views: 303

PDF Views: 4




  • Optimal Allocation of Stratified Sampling Design Using Gradient Projection Method

Abstract Views: 303  |  PDF Views: 4

Authors

M. A. Lone
Division of Agri.stat, SKUAST-K, Kashmir, India
S. A. Mir
Division of Agri.stat, SKUAST-K, Kashmir, India
Imran Khan
Division of Agri.stat, SKUAST-K, Kashmir, India
M. S. Wani
Division of Agri.stat, SKUAST-K, Kashmir, India

Abstract


This article deals with the problem of finding an optimal allocation of sample sizes in stratified sampling design to minimize the cost function. In this paper the iterative procedure of Rosen’s Gradient projection method is used to solve the Non linear programming problem (NLPP), when a non integer solution is obtained after solving the NLPP then Branch and Bound method provides an integer solution.

Keywords


Stratification, Optimal Allocation, Nonlinear Programming, Gradient Projection Method, Branch and Bound Method and Integer Allocation.

References





DOI: https://doi.org/10.13005/ojcst%2F10.01.02