Asymptotic distribution of the reduced rank regression estimator under general conditions

In the regression model Y = + BX + Z with Z unobserved, EZ = 0 and EZZ' = ₙₙ, the least squares estimator of B is B = SₘₗSₗₗ^-1. If the rank of B is known to be k less than the dimensions of Y and X, the reduced rank regression estimator of B, say Bₖ, depends on the first k canonical variates of Y and X. The asymptotic distribution of Bₖ is obtained and compared with the asymptotic distribution of B. The advantage of Bₖ is characterized.