Abstract
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.
Highlights
In sampling literature the problem of determining the sample sizes of the units among strata that minimizes the sampling variance of the estimator of the population mean for a fixed cost or minimizes the total cost of the survey for a fixed precision of the estimator is termed as the problem of allocation
During stratification some strata variances are unknown but may be assumed with equal variances, as discussed by Park et al (2007). They obtained an allocation by using estimated pooled standard deviations and proportional allocation for combined strata
The problem has formulated as multiobjective nonlinear programming problem (MNLPP) to obtain a compromise allocation by minimizing the variances of the estimates of p-population means simultaneously for prefixed budget of the survey
Summary
In sampling literature the problem of determining the sample sizes of the units among strata that minimizes the sampling variance of the estimator of the population mean (or total) for a fixed cost or minimizes the total cost of the survey for a fixed precision of the estimator is termed as the problem of allocation. During stratification some strata variances are unknown but may be assumed with equal variances, as discussed by Park et al (2007) They obtained an allocation by using estimated pooled standard deviations and proportional allocation for combined strata. In the present paper the idea of pooling the standard deviations is extended to obtain a compromise allocation in a multivariate stratified population when the true values of the stratum standard deviations are unknown but the additional information about equality of standard deviations for a specified group of strata and the estimates of the strata standard deviations are available. The problem has formulated as multiobjective nonlinear programming problem (MNLPP) to obtain a compromise allocation by minimizing the variances of the estimates of p-population means simultaneously for prefixed budget of the survey. A simulation study, carried out by Ansari et al (2011), is reconsidered to have two separate numerical examples for illustration and comparison with the proposed allocation
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