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Robust High-Dimensional Regression with Coefficient Thresholding and Its Application to Imaging Data Analysis

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Version 2 2022-12-08, 15:00
Version 1 2022-11-04, 20:00
journal contribution
posted on 2022-12-08, 15:00 authored by Bingyuan Liu, Qi Zhang, Lingzhou Xue, Peter X.-K. Song, Jian Kang

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. Supplementary materials for this article are available online.


Bingyuan Liu, Qi Zhang, and Lingzhou Xue were partially supported by the National Science Foundation (NSF) grants DMS-1811552, DMS-1953189, DMS-2210775, and an National Institutes of Health (NIH) grant R21AI144765. Song’s research was partially supported by an NSF grant DMS-1811734. Kang’s research was partially supported by an NSF grant IIS-2123777 and the NIH grants R01DA048993, R01MH105561, and R01GM124061.


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