ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION COMMENT

Cook, Li and Chiaromonte have introduced the interesting notion of an envelope model, which provides an efficient approach for high-dimensional data analysis. The envelope model looks for the "minimal sufficient response" for the regression of Y on X. Our discussion focuses mainly on a two-staged estimation approach, PLS-MLE, which is workable for n << r + p. The partial-least-squares approach is used to extract an intermediate response subspace. This subspace is assumed to be big enough to contain the envelope subspace, but also small enough to accommodate a stable MLE.