Multivariate stratified sampling by stochastic multiobjective optimisation

TL;DR

This paper formulates the multivariate stratified sampling allocation as a stochastic multiobjective optimization problem, analyzing the asymptotic distribution of sample variances and proposing two solution methods with practical examples.

Contribution

It introduces a novel stochastic multiobjective optimization framework for multivariate stratified sampling allocation, including asymptotic variance analysis and two solution approaches.

Findings

Asymptotic distribution of sample variances derived

Two alternative optimization techniques proposed

Practical example demonstrating methods' effectiveness

Abstract

This work considers the allocation problem for multivariate stratified random sampling as a problem of integer non-linear stochastic multiobjective mathematical programming. With this goal in mind the asymptotic distribution of the vector of sample variances is studied. Two alternative approaches are suggested for solving the allocation problem for multivariate stratified random sampling. An example is presented by applying the different proposed techniques.