Reduced-Rank Regression and Canonical Analysis
本文证明在误差服从正态分布且协方差未知时，降秩回归模型的极大似然分析利用了矩阵理论的一个基本不等式，并揭示了降秩回归与典型分析之间的紧密联系，同时给出了几何解释。
SUMMARY We show that maximum-likelihood analysis of the reduced-rank regression model exploits a fundamental inequality result of matrix theory when a normally distributed error structure with unknown covariance is assumed. This approach closely parallels the corresponding analysis when the covariance matrix is known (Davies and Tso, 1980) and demonstrates straightforwardly the intimate connection between reduced-rank regression and canonical analysis. A geometric interpretation of the analysis is given.