  This paper studies the asymptotic properties of the penalized least squares
estimator using an adaptive group Lasso penalty for the reduced rank
regression. The group Lasso penalty is defined in the way that the regression
coefficients corresponding to each predictor are treated as one group. It is
shown that under certain regularity conditions, the estimator can achieve the
minimax optimal rate of convergence. Moreover, the variable selection
consistency can also be achieved, that is, the relevant predictors can be
identified with probability approaching one. In the asymptotic theory, the
number of response variables, the number of predictors, and the rank number are
allowed to grow to infinity with the sample size.
