Robust High-Dimensional Regression with Coefficient Thresholding and Its Application to Imaging Data Analysis
提出一种结合阈值函数和稳健Huber损失的非凸估计方法，用于处理高维数据中的复杂依赖、重尾和异常值问题，并在青少年脑认知发展研究的fMRI数据中验证了其有效性。
It is important to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible heavy tails and outliers in real-world applications such as imaging data analyses. We propose a new robust high-dimensional regression with coefficient thresholding, in which an efficient nonconvex estimation procedure is proposed through a thresholding function and the robust Huber loss. The proposed regularization method accounts for complex dependence structures in predictors and is robust against heavy tails and outliers in outcomes. Theoretically, we rigorously analyze the landscape of the population and empirical risk functions for the proposed method. The fine landscape enables us to establish both statistical consistency and computational convergence under the high-dimensional setting. We also present an extension to incorporate spatial information into the proposed method. Finite-sample properties of the proposed methods are examined by extensive simulation studies. An application concerns a scalar-on-image regression analysis for an association of psychiatric disorder measured by the general factor of psychopathology with features extracted from the task functional MRI data in the Adolescent Brain Cognitive Development (ABCD) study.