协方差矩阵的乘积及其迹的估计

On the estimation for product of covariance matrices and its trace

摘要:

对于两个不同总体的协方差矩阵，估计其乘积及乘积的迹是统计推断问题的关键步骤. 本文首先构造几个等价估计，同时对于任意的正整数建立了无偏估计.其次，利用等价估计，本文发现了多个常用估计量是相等的. 最后，基于上述发现，证明了两个常用的检验统计量(被用于检验两个协方差矩阵是否相等)是渐近等价的.

Abstract:

In many statistical inference problems involving two populations respectively with covariance matrices and its trace need to be estimated. In this paper, some existing estimators are shown to be equal besides different computational complexities after constructing some equivalent estimates based on the different characterizations of covariance matrix. Moreover, the unbiased and location-invariant estimators are constructed directly for positive integers. The asymptotical equivalence of two existing test statistics for testing the equality of two covariances is provided.