Problem
Research questions and friction points this paper is trying to address.
multivariate linear regression
groupwise predictor envelope
estimation efficiency
Groupwise Predictor Envelope Models for Multivariate Linear Regression
🤖 AI Summary
本文提出了一种组间预测器信封模型，通过共享的预测器信封子空间来提高多变量线性回归中参数估计的效率，并允许各组有特定的回归效应和误差协方差矩阵。
📝 Abstract
Envelope methods improve estimation efficiency in multivariate analysis by isolating low-dimensional structures that contain all the information material to the parameter of interest. In multivariate linear regression with random predictors, predictor envelope models achieve this goal by removing variation in the predictors that is immaterial to the regression. In many applications, observations are naturally divided into several groups, such as treatment groups, regions, or demographic strata, and the regression relationship may differ between groups. Motivated by this setting, we propose a groupwise predictor envelope model for multivariate linear regression. The proposed model assumes that the group-specific regression coefficient matrices are represented through a common predictor envelope subspace while allowing group-specific regression effects and group-specific error covariance matrices. We derive an objective function for estimating the common predictor envelope, obtain the corresponding regression estimators, and establish asymptotic normality together with an explicit asymptotic variance formula. Moreover, we show that the proposed estimator is asymptotically more efficient than the estimator obtained by fitting predictor envelope models separately to each group. This theoretical advantage over the existing work is also demonstrated through simulation studies.
Innovation
Methods, ideas, or system contributions that make the work stand out.
groupwise predictor envelope model
multivariate linear regression
common predictor envelope subspace
asymptotic efficiency
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