Asymptotic distribution of the reduced rank regression estimator under general conditions

Abstract

In the regression model Y = η + BX + Z with Z unobserved, ℰZ = 0 and ℰZZ′ = ΣZZ, the least squares estimator of B is B̂ = SYXS-1XX. 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 B̂k, depends on the first k canonical variates of Y and X. The asymptotic distribution of B̂k is obtained and compared with the asymptotic distribution of B̂. The advantage of B̂k is characterized.