Fixed rank solutions of the matrix equation with statistical applications

Abstract

By applying the canonical correlation decomposition of matrix pairs, the general fixed rank least square solutions of matrix equation Xβ=Y are derived. As statistical applications, an algorithm for computing the least square estimator of the multivariate reduced rank regression model Y=Xβ+ϵ, r(β)=t is given.

Keywords:

• canonical correlation decomposition
• matrix equation
• least square estimator
• multivariate reduced rank regression

AMS Subject Classifications :

• 15A03
• 15A23
• 15A24
• 62J05

Acknowledgements

This work was supported by the Foundation of Shanghai Education Committee (07zz171). The author is grateful for the detailed comments from an anonymous referee.