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Minimum Cost Compromise Mixed Allocation

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

When more than one (say p) characteristics in multivariate stratified population are defined on each unit of the population, the individual optimum allocations may differ widely and can not be used practically. Moreover, there may be a situation such that no standard allocation is advisable to all the strata, for one reason or another. In such a situation, Clark and Steel (J R Stat Soc, Ser D Stat 49(2):197–207, 2000) suggested that different allocations may be used for different groups of strata having some common characteristics for double sampling in stratification. Later on, Ahsan et al. (Aligarh J Stat 25:87–97, 2005) used the same concept in univariate stratified sampling. They minimized the variance of the stratified sample mean for a fixed cost to obtain an allocation and called this allocation “mixed allocation”. In the present paper, a “compromise mixed allocation” is worked out for the fixed precisions of the estimates of the p-population means of a multivariate stratified population. A numerical example is also presented.

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References

  1. Ahsan, M.J., Khan, S.U.: Optimum allocation in multivariate stratified random sampling using prior information. J. Indian Stat. Assoc. 15, 57–67 (1977)

    Google Scholar 

  2. Ahsan, M.J., Khan, S.U.: Optimum allocation in multivariate stratified random sampling with overhead cost. Metrika 29, 71–78 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahsan, M.J., Najmussehar, Khan, M.G.M.: Mixed allocation in stratified sampling. Aligarh J. Stat. 25, 87–97 (2005)

    MathSciNet  Google Scholar 

  4. Ahsan, M.J., Najmussehar, Khan, M.G.M.: Mixed allocation for fixed precision. Pure Appl. Math. Sci. LXIX(1–2), 93–103 (2009)

    MathSciNet  Google Scholar 

  5. Ansari, A.H., Najmussehar, Ahsan, M.J.: On multiple response stratified random sampling design. J. Stat. Sci., Kolkata, India 1(1), 45–54 (2009)

    Google Scholar 

  6. Aoyama, H.: Stratified random sampling with optimum allocation for multivariate populations. Ann. Inst. Stat. Math. 14, 251–258 (1962)

    Article  MathSciNet  Google Scholar 

  7. Arvanitis, L.G., Afonja, B.: Use of the generalized variance and the gradient projection method in multivariate stratified random sampling. Biometrics 27, 119–127 (1971)

    Article  Google Scholar 

  8. Bankier, M.D.: Power allocations: determining sample sizes for subnational areas. Am. Stat. 42, 174–177 (1988)

    Google Scholar 

  9. Bethel, J.: Sample allocation in multivariate surveys. Surv. Methodol. 15(1), 47–57 (1989)

    Google Scholar 

  10. Chatterjee, S.: A note on optimum allocation. Scand. Actuar. J. 50, 40–44 (1967)

    Article  Google Scholar 

  11. Chatterjee, S.: Multivariate stratified surveys. J. Am. Stat. Assoc. 63, 530–534 (1968)

    Article  Google Scholar 

  12. Clark, R.G., Steel, D.G.: Optimum allocation of sample to strata and stages with simple additional constraints. J. R. Stat. Soc., Ser. D Stat. 49(2), 197–207 (2000)

    Article  Google Scholar 

  13. Cochran, W.G.: Sampling Techniques. Wiley, New York (1977)

    MATH  Google Scholar 

  14. Díaz-García, J.A., Cortez, L.U.: Optimum Allocation in Multivariate Stratified Sampling: Multi-Objective Programming. Comunicación Técnica No. I-06-07/28-03-2006 (PE/CIMAT), México (2006)

  15. Folks, J.L., Antle, C.E.: Optimum allocation of sampling units to the strata when there are R responses of interest. J. Am. Stat. Assoc. 60, 225–233 (1965)

    MathSciNet  MATH  Google Scholar 

  16. Jahan, N., Khan, M.G.M., Ahsan, M.J.: A generalized compromise allocation. J. Indian Stat. Assoc. 32, 95–101 (1994)

    Google Scholar 

  17. Khan, M.G.M., Ahsan, M.J., Jahan, N.: Compromise allocation in multivariate stratified sampling: an integer solution. Nav. Res. Logist. 44, 69–79 (1997)

    Article  MATH  Google Scholar 

  18. Khan, M.G.M., Khan, E.A., Ahsan, M.J.: An optimal multivariate stratified sampling design using dynamic programming. Aust. N. Z. J. Stat. 45(1), 107–113 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Khan, M.G.M., Khowaja, S., Ghufran, S., Varshney, R., Ahsan, M.J.: A comparative study of various compromise criteria in multiple quantitative response stratified sampling. J. Stat. Sci. 2(1), 1–12 (2010)

    Google Scholar 

  20. Khan, M.G.M., Maiti, T., Ahsan, M.J.: An optimal multivariate stratified sampling design using auxiliary information: an integer solution using goal programming approach. J. Off. Stat. 26(4), 695–708 (2010)

    Google Scholar 

  21. Kokan, A.R., Khan, S.: Optimum allocation in multivariate surveys: an analytical solution. J. R. Stat. Soc., B 29, 115–125 (1967)

    MathSciNet  MATH  Google Scholar 

  22. Kozak, M.: On sample allocation in multivariate surveys. Commun. Stat., Simul. Comput. 35(4), 901–910 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kreienbrock, L.: Generalized measures of dispersion to solve the allocation problem in multivariate stratified random sampling. Commun. Stat., Theory Methods 22(1), 219–239 (1993)

    Article  MATH  Google Scholar 

  24. LINDO System Inc.: LINGO-User’s Guide. LINDO System Inc., Chicago (2001)

  25. Melaku, A., Sadasivan, G.: L1-norm and other methods for sample allocation in multivariate stratified surveys. Comput. Stat. Data Anal. 5(4), 415–423 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  26. Murthy, M.N.: Sampling Theory and Methods. Statistical Publishing Society, Kolkata (1967)

    MATH  Google Scholar 

  27. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S., Asok, C.: Sampling Theory of Surveys with Applications. Iowa State University Press, Ames. and Indian Society of Agricultural Statistics, New Delhi (1984)

  28. Varshney, R., Ahsan, M.J.: Compromise mixed allocation in multivariate stratified sampling. J. Indian Soc. Agric. Stat. 65(3), 291–296 (2011)

    MathSciNet  Google Scholar 

  29. Yates, F.: Sampling Methods for Censuses and Surveys. Charles Griffin & Co. Ltd., London (1960)

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, 202 002, Uttar Pradesh, India

    Rahul Varshney & M. J. Ahsan

  2. Kejriwal Institute of Management and Development Studies, Namkum, Ranchi, 834010, Jharkhand, India

    A. H. Ansari

Authors
  1. Rahul Varshney
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  2. A. H. Ansari
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  3. M. J. Ahsan
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Correspondence to Rahul Varshney.

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Varshney, R., Ansari, A.H. & Ahsan, M.J. Minimum Cost Compromise Mixed Allocation. J Math Model Algor 12, 373–381 (2013). https://doi.org/10.1007/s10852-012-9215-3

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  • DOI: https://doi.org/10.1007/s10852-012-9215-3

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