Mathematical Sciences: Investigations on Multivariate Statistical Decision Theory

数学科学：多元统计决策理论研究

• 批准号: 9000999
• 负责人: Andrew Rukhin
• 金额: $ 6万
• 依托单位: University of Maryland Baltimore County
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000999&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Investigations; Multivariate; Statistical

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.

该项目旨在研究多元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特征。正态分布的目标是找到可接受的估计量和极小极大估计量，并确定产生此类过程的先验分布。 将对这些问题进行渐近研究，并详细研究由此产生的正态正态均值估计问题。将研究二元正态分布样本的最大散布的渐近分布及其渐近效率。