Optimum stratification for a generalized auxiliary variable proportional allocation under a superpopulation model

Abstract

Under a heteroscedastic regression superpopulation (HRS) model considered by Rao, Gupt obtained several model-based allocations including two generalized allocations, one of which is generalized auxiliary variable proportional allocation (GAVPA). In this article, we investigate the problem of optimum stratification for GAVPA under the HRS model. Equations giving optimum points of stratification (OPS) have been derived for the GAVPA by minimizing the expected variance under the HRS model. A few methods of finding approximate solutions to these equations have also been derived. Numerical illustrations of the equations and methods of approximation have been done by using generated and live populations. All these methods of stratification are found to stratify efficiently not only less skewed and lower level of heteroscedastic but also highly skewed and higher level of heteroscedastic populations in giving OPS.

Keywords:

• Auxiliary variable
• minimal equations
• optimum strata boundaries (OSB)
• optimum stratification
• stratified simple random sampling with and without replacement designs (SRSWR & SRSWOR)
• superpopulation models

Acknowledgement

We express our sincere gratitude to the Editor in Chief and the anonymous reviewers for the valuable comments and suggestions which led to significant improvement of the paper.