Envelopes for multivariate linear regression with linearly constrained coefficients
针对系数矩阵列向量受限于已知子空间的约束多元线性模型，提出了一种新的包络估计量，通过模拟和沙门氏菌感染研究证明了其相比标准估计量在偏差和效率上的优势。
Abstract 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.