Abstract

In this paper, we consider a situation when the population variances of the auxiliary variable in the first stage units selected in a sample are known in addition to the known population means of the auxiliary variable. The higher order calibration weights which make use of both the population variances and population means at the estimation stage for both the first stage units and the second stage units selected in the sample are derived. The resultant estimator is found to be consistent estimator, and has variance smaller than the existing estimators in the literature. The percent relative efficiency of the proposed estimator over the linear regression estimator has been demonstrated through numerical comparisons.

摘要

在本文中，我们考虑一种情况，即除了已知的辅助变量的总体均值外，样本中选择的第一阶段单元中辅助变量的总体方差已知。推导出样本中选择的第一阶段单元和第二阶段单元在估计阶段利用总体方差和总体均值的高阶校准权重。结果估计量被发现是一致的估计量，并且方差小于文献中现有的估计量。已通过数值比较证明了所提出的估计器相对于线性回归估计器的相对效率百分比。