A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection.

中文翻译：

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具有线性约束系数的多元线性回归的包络线

约束多元线性模型是其系数矩阵的列被约束位于已知子空间中的多元线性模型。此类模型包括通常用于研究生长曲线和纵向数据的模型。已经提出了包络方法来提高无约束多元线性模型的估计效率，但尚未开发用于约束模型。我们在本文中追求这一发展。我们首先在偏差和效率方面将标准包络估计器与约束多元模型产生的标准估计器进行比较。为了进一步提高效率，我们提出了一种基于约束多元模型的新型包络估计器。我们通过模拟和研究益生菌减少沙门氏菌感染的能力来展示我们建议的优势。