On Compromise Mixed Allocation in Multivariate Stratified Sampling with Random Parameters

Abstract

For estimating the population mean Clark and Steel (Stat. 49, 1970–207 2000) worked out the optimum allocation of sample sizes to strata and stages with simple additional constraints to use different type of allocations in different strata. Ahsan et al. (Aligarh J. Statist. 25, 87–97 2005) used the same idea to work out optimum allocation in univariate stratified sampling and called it a ‘Mixed Allocation’. Later on Varshney and Ahsan (J. Indian Soc. Agr. Stat. 65(3), 291–296, 2011) extended this work for multivariate stratified sampling and called it a compromise mixed allocation. This article presents a more realistic approach to the compromise mixed allocation by formulating the problem as a Stochastic Nonlinear Programming Problem in which the stratum-wise measurement costs and the sample stratum standard deviations are independent random variables with known probability distributions. The application of this approach is exhibited through a numerical example with normal distributions of the random parameters. The proposed compromise mixed allocation is compared with some other well known compromise allocations available in multivariate stratified sampling literature. It is found that the author’s proposed compromise mixed allocation is the most efficient allocation among the discussed allocations. A simulation study is also carried out to support the claim made by the authors on the basis of the results of the numerical example.