References
- Ahsan , MJ and Khan , SU . 1982 . Optimum allocation in multivariate stratified random sampling with overhead cost . Metrika , 29 : 71 – 78 .
- Arthanari , TS and Dodge , Y . 1991 . Mathematical Programming in Statistics , New York : John Wilwy & Sons .
- Arvanitis , LG and Afonja , B . 1971 . Use of the generalized variance and the gradient projection method in multivariate stratified sampling . Biometrics , 27 : 119 – 127 .
- Bazaraa , MS , Sherali , HD and Shetty , CM . 2006 . Nonlinear Programming: Theory and Algorithms , 3rd , New Jersey : Wiley-Interscience .
- Bethal , J . 1985 . An optimum allocation algorithm for multivariate surveys . Proceedings of the Section on Survey Methods Research, American Statistical Association, , : 209 – 212 .
- Bethal , J . 1989 . Sample allocation in multivariate surveys . Surv. Methodol. , 15 : 47 – 57 .
- Charnes , A and Cooper , WW . 1963 . Deterministic equivalents for optimizing and satisficing under chance constraints . Oper. Res. , 11 : 18 – 39 .
- Chromy , J . 1987 . Design optimization with multiple objectives . Proceedings of the Section on Survey Methods Research, American Statistical Association, , : 194 – 199 .
- Cochran , WG . 1977 . Sampling Techniques , New York : Wiley .
- Díaz-García , JA and Garay Tapia , MM . 2007 . Optimum allocation in stratified surveys: Stochastic programming . Comput. Stat. Data Anal. , 51 : 3016 – 3026 .
- Díaz García , JA and Ramos-Quiroga , R . Optimum allocation in multivariate stratified random sampling: Stochastic matrix optimisation, Stat. Neerlendica (2012), to appear. ,
- Díaz García , JA , Ramos-Quiroga , R and Cabrera-Vicencio , E . 2005 . Stochastic programming methods in the response surface methodology . Comput. Stat. Data Anal. , 49 : 837 – 848 .
- Díaz-García , JA and Ulloa , CL . 2008 . Multi-objective optimisation for optimum allocation in multivariate stratified sampling . Surv. Method. , 34 : 215 – 222 .
- Hájek , J . 1961 . Some extensions of the Wald-Wolfowitz-Noether theorem . Ann. Math. Stat. , 32 : 506 – 523 .
- Jahan , N , Khan , MGM and Ahsan , MJ . 1994 . A generalized compromise allocation . J. Ind. Stat. Assoc. , 32 : 95 – 101 .
- Kataoka , S . 1963 . A stochastic programming model . Econometrica , 31 : 181 – 196 .
- Kazemzadeh , RB , Bashiri , M , Atkinson , AC and Noorossana , R . 2008 . A general framework for multiresponse optimization problems based on goal programming . Eur. J. Oper. Res. , 189 : 421 – 429 .
- Khan , MGM and Ahsan , MJ . 2003 . A note on optimum allocation in multivariate stratified sampling . South Pac. J. Nat. Sci. , 21 : 91 – 95 .
- Khan , MGM , Ahsan , MJ and Jahan , N . 1997 . Compromise allocation in multivariate stratified sampling: An integer solution . Naval Res. Logist. , 44 : 69 – 79 .
- Khan , MGM , Khan , EA and Ahsan , MJ . 2003 . An optimal multivariate stratified sampling design using dynamic programming . Aust. New Zealand J. Stat. , 45 : 107 – 113 .
- Khan , MGM , Maiti , T and Ahsan , MJ . 2010 . An optimal multivariate stratified sampling design using auxiliary information: An integer solution using goal programming approach . J. Off. Stat. , 26 : 695 – 708 .
- Khuri , AI and Cornell , JA . 1987 . Response Surfaces: Designs and Analyses , New York : Marcel Dekker .
- Melaku , A . 1986 . Asymptotic normality of the optimal allocation in multivariate stratified random sampling . Indian J. Stat. Ser. B , 48 : 224 – 232 .
- Miettinen , KM . 1999 . Non Linear Multiobjective Optimization , Boston : Kluwer Academic Publishers .
- Muirhead , RJ . 1982 . “ Aspects of Multivariate Statistical Theory ” . In Wiley Series in Probability and Mathematical Statistics , New York : John Wiley & Sons .
- Neyman , J . 1934 . On the two different aspects of the representative methods: The method of stratified sampling and the method of purposive selection . J. Roy. Stat. Soc. , 97 : 558 – 625 .
- Prékopa , A . 1970 . “ On probabilistic constrained programming ” . In Proceedings of the Princeton Symposium on Mathematical Programming , 113 – 138 . Princeton , NJ : Princeton University Press .
- Prékopa , A . 1978 . “ The use of stochastic programing for the solution of some problems in statistics and probability ” . In Technical Summary Report #1834 , University of Wisconsin-Madison, Mathematical Research Center .
- Prékopa , A . 1995 . “ Stochastic Programming ” . In Mathematics and its Applications , Dordrecht, The Netherlands : Kluwer Academic Publishers .
- Rao , CR . 1973 . Linear Statistical Inference and its Applications , 2nd , New York : John Wiley & Sons .
- Rao , SS . 1978 . Optimization Theory and Applications , New Delhi : Wiley Eastern Limited .
- Ríos , S , Ríos Insua , S and Ríos Insuay , MJ . 1989 . “ Procesos de Decisión Multicriterio ” . In EUDEMA , Spanish : Madrid .
- Stancu-Minasian , IM . 1984 . Stochastic Programming , Dordrecht : Reidel P. Co. .
- Steuer , RE . 1986 . Multiple Criteria Optimization: Theory, Computation and Applications , New York : John Wiley .
- Stuart , A . 1954 . A simple presentation of optimum sampling results . J. R. Stat. Soc. B , 16 : 239 – 241 .
- Sukhatme , PV , Sukhatme , BV , Sukhatme , S and Asok , C . 1984 . Sampling Theory of Surveys with Applications , 3rd , Iowa State University Press, Ames, Iowa .
- Thompson , ME . 1997 . Theory of Sample Surveys , London : Chapman & Hall .
- Uryasev , S and Pardalos , PM . 2001 . Stochastic Optimization , Dordrecht, The Netherlands : Kluwer Academic Publishers .
- Winston , WL . 1995 . Introduction to Mathematical Programming: Applications and Algorithms , Belmont, CA : Duxbury Press .