统计学中的若干矩阵研究

Some Matrix Research in Statistics

矩阵论在现代统计的许多分支都有着广泛的应用,同时统计学又提出了许多新的有关矩阵论的研究课题,刺激了矩阵论的发展。本文旨在向读者介绍矩阵论中并与统计学密切有关的如下三方面的新发展:矩阵的{2}广义逆、矩阵的降秩逼近和偏序关系,并且讨论了这些结果的统计应用。特别是在多元分析和线性模型参数估计中的应用。

Matrix theory has come into wide use in many branches of the modern statistics, moreover their developements have been caused by many concerning problemsproposed in the statistics. In this paper, three further problems related to statistics, such as{2} - generalized inverse, the singular approximating and the ordering relation of matrices are in troduced in the matrix theory. Bseides, some application of the above results are also discussed in the statistics, especially in the multivariate analysis and the parameter estimate of the linear model.