论文标题
协方差回归
Covariance-on-Covariance Regression
论文作者
论文摘要
本手稿中引入了协方差回归模型。假定存在（至少）（至少）关于结果协方差矩阵和预测器协方差矩阵的一对线性投影，以便对数线性模型在投影空间中的方差以及其他兴趣的协方差链接。提出了一种普通的最小平方估计器，以同时识别投影和估计模型系数。在规律性条件下，提出的估计量在渐近一致。通过模拟研究证明了所提出的方法的优越性能优于现有方法。应用于人类Connectome项目老化研究中收集的数据时，该方法确定了三对大脑网络，其中静息状态网络中的功能连接可以预测相应的任务状态网络中的功能连接。这三个网络对应于全局信号网络，与任务相关的网络和任务无关的网络。这些发现与有关大脑功能的现有知识一致。
A Covariance-on-Covariance regression model is introduced in this manuscript. It is assumed that there exists (at least) a pair of linear projections on outcome covariance matrices and predictor covariance matrices such that a log-linear model links the variances in the projection spaces, as well as additional covariates of interest. An ordinary least square type of estimator is proposed to simultaneously identify the projections and estimate model coefficients. Under regularity conditions, the proposed estimator is asymptotically consistent. The superior performance of the proposed approach over existing methods are demonstrated via simulation studies. Applying to data collected in the Human Connectome Project Aging study, the proposed approach identifies three pairs of brain networks, where functional connectivity within the resting-state network predicts functional connectivity within the corresponding task-state network. The three networks correspond to a global signal network, a task-related network, and a task-unrelated network. The findings are consistent with existing knowledge about brain function.
