This study is concerned with construction of the generalized multivariate exponential estimator for estimating a population mean vector in the two-phase sampling using multi-auxiliary variables when population information for some auxiliary variables is not available. The optimum conditions which provide the matrix of minimum variance–covariance are obtained for the suggested estimator. Further, a vector of the biases is also provided. Some deduced univariate and multivariate estimators are also shown as special cases of the suggested multivariate exponential estimator. The simulation study is conducted using the artificial symmetric and asymmetric distributions to show that the suggested multivariate estimator performs more efficiently than the existing multivariate estimator. Two real-life examples are used to show the usefulness of the proposed multivariate estimators.

这项研究与广义多元指数估计器的构造有关，该估计器用于在无法获得某些辅助变量的总体信息的情况下，使用多辅助变量来估计两阶段采样中的总体均值向量。为建议的估计量提供了提供最小方差-协方差矩阵的最佳条件。此外，还提供了偏差的向量。一些推导的单变量和多变量估计量也显示为建议的多元指数估计量的特殊情况。使用人工对称和非对称分布进行了仿真研究，结果表明，建议的多元估计器比现有的多元估计器更有效。