3 We incorporate the idea of reduced rank envelope [7] to elliptical multivariate linear regres4 sion to improve the efficiency of estimation. The reduced rank envelope model takes advantage 5 of both reduced rank regression and envelope model, and is an efficient estimation technique in 6 multivariate linear regression. However, it uses the normal log-likelihood as its objective func7 tion, and is most effective when the normality assumption holds. The proposed methodology 8 considers elliptically contoured distributions and it incorporates this distribution structure into 9 the modeling. Consequently, it is more flexible and its estimator outperforms the estimator de10 rived for the normal case. When the specific distribution is unknown, we present an estimator 11 that performs well as long as the elliptically contoured assumption holds. 12

中文翻译：

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椭圆多元线性回归的包络

3 我们将降低秩包络 [7] 的思想结合到椭圆多元线性回归中，以提高估计效率。降阶包络模型利用降阶回归和包络模型的 5 优点，是 6 多元线性回归中的一种有效估计技术。然而，它使用正态对数似然作为其目标函数，并且在正态性假设成立时最有效。所提出的方法 8 考虑了椭圆轮廓分布，并将这种分布结构合并到 9 建模中。因此，它更加灵活，并且它的估计器优于为正常情况设计的估计器。当特定分布未知时，我们提出一个估计器 11，只要椭圆轮廓假设成立，它就会表现良好。12