Estimation of graphical models for skew continuous data
提出一种基于节点回归的方法，通过线性模型和投影寻踪回归处理残差，估计非高斯偏斜连续数据的图结构，并证明变量数随样本量发散时图估计的一致性。
Abstract We consider a new approach for estimating non‐Gaussian undirected graphical models. Specifically, we model continuous data from a class of multivariate skewed distributions, whose conditional dependence structure depends on both a precision matrix and a shape vector. To estimate the graph, we propose a novel estimation method based on nodewise regression: we first fit a linear model, and then fit a one component projection pursuit regression model to the residuals obtained from the linear model, and finally threshold appropriate quantities. Theoretically, we establish error bounds for each nodewise regression and prove the consistency of the estimated graph when the number of variables diverges with the sample size. Simulation results demonstrate the strong finite sample performance of our new method over existing methods for estimating Gaussian and non‐Gaussian graphical models. Finally, we demonstrate an application of the proposed method on observations of physicochemical properties of wine.