Advertisement

On Compromise Mixed Allocation in Multivariate Stratified Sampling with Random Parameters

  • Ummatul Fatima
  • Rahul Varshney
  • Siddiqui Najmussehar
  • Mohammad Jameel Ahsan
Article
  • 93 Downloads

Abstract

For estimating the population mean Clark and Steel (Stat. 49, 1970–207 2000) worked out the optimum allocation of sample sizes to strata and stages with simple additional constraints to use different type of allocations in different strata. Ahsan et al. (Aligarh J. Statist. 25, 87–97 2005) used the same idea to work out optimum allocation in univariate stratified sampling and called it a ‘Mixed Allocation’. Later on Varshney and Ahsan (J. Indian Soc. Agr. Stat. 65(3), 291–296, 2011) extended this work for multivariate stratified sampling and called it a compromise mixed allocation. This article presents a more realistic approach to the compromise mixed allocation by formulating the problem as a Stochastic Nonlinear Programming Problem in which the stratum-wise measurement costs and the sample stratum standard deviations are independent random variables with known probability distributions. The application of this approach is exhibited through a numerical example with normal distributions of the random parameters. The proposed compromise mixed allocation is compared with some other well known compromise allocations available in multivariate stratified sampling literature. It is found that the author’s proposed compromise mixed allocation is the most efficient allocation among the discussed allocations. A simulation study is also carried out to support the claim made by the authors on the basis of the results of the numerical example.

Keywords

Multivariate stratified surveys Mixed allocation Stochastic programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahsan, M.J., Najmussehar, Khan, M.G.M.: Mixed allocation in stratified sampling. Aligarh J. Statist. 25, 87–97 (2005)MathSciNetGoogle Scholar
  2. 2.
    Chatterjee, S.: A note on optimum allocation. Skand. Akt. 50, 40–44 (1967)Google Scholar
  3. 3.
    Clark, R.G., Steel, D.G.: Optimum allocation of samples to strata and stages with simple additional constraints. Stat. 49, 197–207 (2000)Google Scholar
  4. 4.
    Cochran, W.G.: Sampling Techniques. Wiley, New York (1977)MATHGoogle Scholar
  5. 5.
    Díaz-García, J.A., Gary-Tápia, M.M.: Optimum allocation in stratified surveys: stochastic programming. Comput. Statist. Data Anal. 51, 3016–3026 (2007)CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    Jahan, N., Khan, M.G.M., Ahsan, M.J.: A generalized compromise allocation. J. Indian Statist. Assoc. 32, 95–101 (1994)Google Scholar
  7. 7.
    Kozak, M.: On sample allocation in multivariate surveys. Comm. Statist. Simul. Comput. 35, 901–910 (2006a)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Kozak, M.: Multivariate sample allocation: application of random search method. Stat. Trans. 7(4), 889–900 (2006b)Google Scholar
  9. 9.
    LINGO: LINGO-User’s Guide. Published by LINDO SYSTEM INC., 1415, North Dayton Street, Chicago, Illinois, 60622, USA (2001)Google Scholar
  10. 10.
    Melaku, A.: Asymptotic normality of the optimal allocation in multivariate stratified random sampling. Sankhya B 48(2), 224–232 (1986)MathSciNetMATHGoogle Scholar
  11. 11.
    Rao, S.S.: Optimization Theory and Applications. Wiley Eastern limited, New Delhi (1977)Google Scholar
  12. 12.
    R Core Team: A language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria, http://www.r-project.org/ (2012)
  13. 13.
    Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S., Asok, C.: Sampling Theory of Surveys with Applications. Iowa State University Press, Iowa, U.S.A. and Indian Society of Agricultural Statistics, New Delhi (1984)Google Scholar
  14. 14.
    Varshney, R., Ahsan, M.J.: Compromise mixed allocation in multivariate stratified sampling. J. Indian Soc. Agr. Stat. 65(3), 291–296 (2011)MathSciNetGoogle Scholar
  15. 15.
    Yates, F.: Sampling Methods for Censuses and Surveys. Charles Griffin and Co. Ltd., London (1960)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ummatul Fatima
    • 1
  • Rahul Varshney
    • 2
  • Siddiqui Najmussehar
    • 1
  • Mohammad Jameel Ahsan
    • 1
  1. 1.Department of Statistics and Operations ResearchAligarh Muslim UniversityAligarhIndia
  2. 2.Department of MathematicsGalgotias UniversityGreater NoidaIndia

Personalised recommendations