Mathematical Sciences: Investigations on Multivariate Statistical Decision Theory

该项目旨在研究多变量随机向量的未知统计协方差矩阵的估计。它包括广义方差、判别系数、相关性和精度矩阵等相关性质。在正态分布的情况下，目标是找到可接受的和极大极小估计，并确定引起这种过程的先验分布。将对这些问题进行渐近研究，并详细研究由此产生的正态平均估计问题。我们将研究二元正态分布样本的最大分布的渐近分布及其渐近效率。

The project is intended to investigate the estimation of an unknown statistical covariance matrix of a multivariate random vector. It includes related charactertistics such as generalized variance, discriminant coefficients, correlation and precision matrices. The goal in the case of the normal distribution is to find admissible and minimax estimators and to determine prior distributions which give rise to such procedures. The asymptotic study of these problems is to be performed and the resulting problem of positive normal mean estimation will be studied in detail. The asymptotic distribution of the maximum spread for a sample from a bivariate normal distribution will be studied along with its asymptotic efficiency.