Optimum allocation in multivariate stratified random sampling: Stochastic matrix optimisation

TL;DR

This paper formulates the optimal allocation problem in multivariate stratified sampling as a stochastic matrix integer programming problem, establishing asymptotic normality of sample covariance matrices and proposing solution methods.

Contribution

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

Findings

Asymptotic normality of sample covariance matrices established

Proposed stochastic matrix integer programming approach

Example demonstrating the effectiveness of the methods

Abstract

The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sample covariance matrices for each strata is established. Some alternative approaches are suggested for its solution. An example is solved by applying the proposed techniques.