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.

摘要

在 Rao 考虑的异方差回归超群 (HRS) 模型下，Gupt 获得了几个基于模型的分配，包括两个广义分配，其中一个是广义辅助变量比例分配 (GAVPA)。在本文中，我们研究了 HRS 模型下 GAVPA 的最佳分层问题。通过最小化 HRS 模型下的预期方差，为 GAVPA 导出了给出最佳分层点 (OPS) 的方程。还推导出了一些找到这些方程的近似解的方法。通过使用生成的和活的种群已经完成了方程和近似方法的数值说明。