An optimum multivariate-multiobjective stratified sampling design

Summary It is well known that in stratified sampling design when the measurement cost does not vary from stratum to stratum, an estimate of population mean or total constructed from a sample selected according to Neyman allocation is the most precise estimate. But unfortunately the practical use of Neyman allocation suffers from a number of limitations. The most serious of all is the absence of the true values of the stratum standard deviations. When the strata standard deviations are unknown but we have additional information about the equality of standard deviations between some of the strata, we can use this information to increase the precision of the estimate by pooling the strata with equal standard deviations as a single stratum and using Neyman and proportional allocations together. This paper studies the case of multiple pooling of the standard deviations in a multivariate stratified sampling when the number of strata is more than three. The problem is formulated as a Multiobjective Nonlinear Programming Problem. A solution procedure is developed using Goal Programming approach. For computation purpose, the software LINGO is used.