Envelope for Elliptical Multivariate Linear Regression

Forzani, L. and Su, Z.

Statistica Sinica, to appear.

We incorporate the idea of reduced rank envelope (Cook et al., 2015) to elliptical multivariate linear regression to improve the efficiency of estimation. The reduced rank envelope model takes advantage of both reduced rank regression and envelope model, and is an efficient estimation technique in multivariate linear regression. However, it uses the normal log-likelihood as its objective function, and is most effective when the normality assumption holds. The proposed methodology considers elliptically contoured distributions and it incorporates this distribution structure into the modeling. Consequently, it is more flexible and its estimator outperforms the estimator derived for the normal case. When the specific distribution is unknown, we present an estimator that performs well as long as the elliptically contoured assumption holds.


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