Abstract: We incorporate a reduced-rank envelope in an elliptical multivariate linear regression to improve the efficiency of estimation. The reduced-rank envelope model takes advantage of both a reduced-rank regression and the envelope model, and is an efficient estimation technique in multivariate linear regressions. However, it uses the normal log-likelihood as its objective function, and is most effective when the normality assumption holds. The proposed methodology incorporates elliptically contoured distributions. Consequently, it is more flexible, and its estimator outperforms that of the normal case. When the specific distribution is unknown, we present an estimator that performs well, as long as the ellipticity assumption holds.

Key words and phrases: Elliptical multivariate linear regression, envelopes, reduced-rank regression.