An Optimum Multivariate-Multiobjective Stratified Sampling Design: Fuzzy Programming Approach

In stratified sampling design when the cost of measuring the units is not significant in each stratum, the estimation of population mean or total constructed from a selected sample according to Neyman allocation is advisable. In general the practical use of Neyman allocation suffers from a number of limitations, when there is no information about strata standard deviations except about the equality of standard deviations between some of the strata, then the precision of the estimate may be increased by pooling the strata with equal standard deviations as a single stratum and the problem of allocation is resolved by using Neyman and proportional allocations simultaneously. In this paper the case of multiple pooling of the standard deviations of the estimates in a multivariate stratified sampling for more than three strata. The problem is formulated as a Multiobjective Nonlinear Programming Problem and its solution procedure is suggested by using Fuzzy Programming approach.

[1]  M. J. Ahsan,et al.  Mixed allocation in stratified sampling , 2005 .

[2]  Lothar Kreienbrock,et al.  Generalized measures of dispersion to solve the allocation problem in multivariate stratified random sampling , 1992 .

[3]  M. J. Ahsan,et al.  Theory & Methods: An Optimal Multivariate Stratified Sampling Design Using Dynamic Programming , 2003 .

[4]  M. J. Ahsan,et al.  An optimum multivariate stratified double sampling design in presence of non-response , 2012, Optim. Lett..

[5]  R. Tiwari,et al.  Fuzzy goal programming- an additive model , 1987 .

[6]  Liliana Ulloa Cortez,et al.  OPTIMUM ALLOCATION IN MULTIVARIATE STRATIFIED SAMPLING: MULTI-OBJECTIVE PROGRAMMING , 2006 .

[7]  M. J. Ahsan,et al.  Optimum allocation in multivariate stratified random sampling with overhead cost , 1982 .

[8]  P. Mahalanobis.  On large-scale sample surveys , 1944, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[9]  Use of the Generalized Variance and the Gradient Projection Method in Multivariate Stratified Sampling , 1971 .

[10]  M. Kozak.  On Sample Allocation in Multivariate Surveys , 2006 .

[11]  Michael D. Bankier,et al.  Power Allocations: Determining Sample Sizes for Subnational Areas , 1988 .

[12]  Compromise Allocation in Univariate Stratified Sampling , 2007 .

[13]  M. J. Ahsan,et al.  An optimum multivariate-multiobjective stratified sampling design , 2011 .

[14]  A. Stuart.  A SIMPLE PRESENTATION OF OPTIMUM SAMPLING RESULTS , 1954 .

[15]  Samprit Chatterjee,et al.  A note on optimum allocation , 1967 .

[16]  Samprit Chatterjee,et al.  Multivariate Stratified Surveys , 1968 .

[17]  J. Neyman.  On the Two Different Aspects of the Representative Method: the Method of Stratified Sampling and the Method of Purposive Selection , 1934 .

[18]  S. P. Ghosh,et al.  A Note on Stratified Random Sampling with Multiple Characters , 1958 .

[19]  Mohammed G. M. Khan,et al.  Integer compromise allocation in multivariate stratified surveys , 2015, Ann. Oper. Res..

[20]  A. R. Kokan,et al.  Optimum Allocation in Multivariate Surveys : An Analytical Solution , 1967 .

[21]  Tore Dalenius.  Sampling in Sweden : contributions to the methods and theories of sample survey practice , 1957 .

[22]  M. J. Ahsan,et al.  On Compromise Mixed Allocation in Multivariate Stratified Sampling with Random Parameters , 2014, J. Math. Model. Algorithms Oper. Res..

[23]  Marcin Kozak,et al.  MULTIVARIATE SAMPLE ALLOCATION: APPLICATION OF RANDOM SEARCH METHOD , 2006 .

[24]  H. Aoyama,et al.  Stratified random sampling with optimum allocation for multivariate population , 1962 .

[25]  J. A. Díaz-García,et al.  Multi-objective optimisation for optimum allocation in multivariate stratified sampling , 2008 .

[26]  A. Melaku,et al.  L 1 -norm and other methods for sample allocation in multivariate stratified surveys , 1987 .

[27]  M. J. Ahsan,et al.  Compromise allocation in multivariate stratified sampling : An integer solution , 1997 .

[28]  Charles E. Antle,et al.  Optimum Allocation of Sampling Units to Strata When There are R Responses of Interest , 1965 .

[29]  F. Yates,et al.  Sampling Methods for Censuses and Surveys , 1950 .