Parameter estimation for reduced-rank multivariate linear regressions in the presence of correlated noise

This paper considers the problem of estimating the parameters in a reduced-rank multivariate linear regression. Reduced rank linear regression has applications in areas such as econometrics, statistics and signal processing. The proposed method can accommodate noise with both temporal and spatial correlation. It relies on a weighted low rank approximation of the full rank regression matrix obtained from a least squares fit to the data. Numerical studies suggest performance comparable to the maximum likelihood solution proposed in P. Stoica et al. [1996] for the white noise case, and an improvement when the noise is temporally correlated.