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Original Articles

Multi-objective optimization for optimum allocation in multivariate stratified sampling with quadratic cost

, &
Pages 1789-1798 | Received 23 Feb 2011, Accepted 07 Jun 2011, Published online: 14 Jul 2011

References

  • Csenki , A. 1997 . Optimum allocation in stratified random sampling via Holder's inequality, Statistician , 46 : 439 – 441 .
  • Beardwood , J. , Halton , J. H. and Hammersley , J. M. 1959 . The shortest path through many points . Proc. Cambridge Philos. Soc. , 55 : 299 – 327 . (doi:10.1017/S0305004100034095)
  • Neyman , J. 1934 . On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection . J. R. Stat. Soc. , 97 : 558 – 625 . (doi:10.2307/2342192)
  • Dalenius , T. 1953 . The multivariate sampling problem . Skand. Actuarietidskrift , 36 : 92 – 102 .
  • Dalenius , T. 1957 . “ Sampling in Sweden ” . In Contributions to the Methods and Theories of Sample Survey Practice , Stockholm : Almqvist and Wicksell .
  • Ghosh , S. P. 1958 . A note on stratified random sampling with multiple characters . Calcutta Statist. Assoc. Bull. , 8 : 81 – 89 .
  • Yates , F. 1960 . Sampling Methods for Censuses and Surveys , 3 , London : Charles Griffin and Co. .
  • Aoyama , H. 1963 . Stratified random sampling with optimum allocation for multivariate populations . Ann. Inst. Statist. Math. , 14 : 251 – 258 . (doi:10.1007/BF02868647)
  • Gren , J. 1964 . Some methods of sample allocation in multivariate stratified sampling . Przeglad Statystyczny , 11 : 361 – 369 . (in Polish)
  • Gren , J. 1966 . Some application of non-linear programming in sampling methods . Przeglad Statystyczny , 13 : 203 – 217 . (in Polish)
  • Folks , J. L. and Antle , C. E. 1965 . Optimum allocation of sampling units to the strata when there are R responses of interest . J. Amer. Statist. Assoc. , 60 : 225 – 233 .
  • Hartley , H. O. Multiple Purpose Optimum Allocation in Stratified Sampling . Proceedings of the Social Statistics Section, American Statistical Association , pp. 258 – 261 .
  • Kokan , A. R. and Khan , S. U. 1967 . Optimum allocation in multivariate surveys: An analytical solution . J. R. Stat. Soc. Ser. , B 29 : 115 – 125 .
  • Chatterjee , S. 1972 . A study of optimum allocation in multivariate stratified surveys . Skand. Actuarietidskrift , 55 : 73 – 80 .
  • Ahsan , M. J. and Khan , S. U. 1977 . Optimum allocation in multivariate stratified random sampling using prior information . J. Indian Statist. Assoc. , 15 : 57 – 67 .
  • Ahsan , M. J. and Khan , S. U. 1982 . Optimum allocation in multivariate stratified random sampling with overhead cost . Metrika , 29 : 71 – 78 . (doi:10.1007/BF01893366)
  • Chromy , J. R. Design Optimization with Multiple Objectives . Proceedings of the Survey Research Methods Section, American Statistical Association , pp. 194 – 199 .
  • Wywial , J. 1988 . Minimizing the spectral radius of means vector from sample variance–covariance matrix sample allocation between strata . Prace Naukowe Akademii Ekonomicznej we Wroclawiu , 404 : 223 – 235 . (in Polish)
  • Bethel , J. 1989 . Sample allocation in multivariate surveys . Surv. Methodol. , 15 : 47 – 57 .
  • Kreienbrock , L. 1993 . Generalized measures of dispersion to solve the allocation problem in multivariate stratified random sampling . Comm. Statist. Theory Methods , 22 ( 1 ) : 219 – 239 .
  • Jahan , N. , Khan , M. G.M. and Ahsan , M. J. 1994 . A generalized compromise allocation . J. Indian Statist. Assoc. , 32 : 95 – 101 .
  • Khan , M. G.M. , Ahsan , M. J. and Jahan , N. 1997 . Compromise allocation in multivariate stratified sampling: An integer solution . Naval Res. Logist. , 44 : 69 – 79 . (doi:10.1002/(SICI)1520-6750(199702)44:1<69::AID-NAV4>3.0.CO;2-K)
  • Khan , M. G.M. , Khan , E. A. and Ahsan , M. J. 2003 . An optimal multivariate stratified sampling design using dynamic programming . Aust. NZ J. Stat. , 45 ( 1 ) : 107 – 113 . (doi:10.1111/1467-842X.00264)
  • Ahsan , M. J. , Najmussehar and Khan , M. G.M. 2005 . Mixed allocation in stratified sampling . Aligarh J. Statist. , 25 : 87 – 97 .
  • Kozak , M. 2006 . On sample allocation in multivariate surveys . Comm. Statist. Simulation Comput. , 35 : 901 – 910 . (doi:10.1080/03610910600880286)
  • Díaz-García , J. A. and Ulloa , C. L. 2006 . “ Optimum allocation in multivariate stratified sampling: Multi-objective programming ” . In Comunicación Técnica No. I-06-07/28-03-206 (PE/CIMAT) Guanajuato , , México
  • Díaz-García , J. A. and Ulloa , C. L. 2008 . Multi-objective optimization for optimum allocation in multivariate stratified sampling . Surv. Methodol. , 34 ( 2 ) : 215 – 222 .
  • Ansari , A. H. , Najmussehar and Ahsan , M. J. 2009 . On multiple response stratified random sampling design . Int. J. Statist. Sci. , 1 ( 1 ) : 1 – 11 .
  • Ríos , S. , Ríos Insua , S. and Ríos Insua , M. J. 1989 . Procesos de decisión Multicriterio , Vol. in Spanish , Madrid : EUDEMA .
  • Miettinen , K. M. 1999 . Non-Linear Multiobjective Optimization , Boston , MA : Kluwer Academic Publishers .
  • Steuer , R. E. 1986 . Multiple Criteria Optimization: Theory, Computation and Applications , New York : John Wiley & Sons .
  • Khuri , A. I. and Cornell , J. A. 1986 . Response Surface: Designs Analysis , New York : Marcel Dekker, Inc .

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