Sparse Learning and Structure Identification for Ultrahigh-Dimensional Image-on-Scalar Regression

• 成果类型: Article
• 署名作者: Li, Xinyi; Wang, Li; Wang, Huixia Judy
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; Iowa State University; George Washington University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1753523
• 发表日期: 2021
• 页码: 1994-2008
• 关键词: varying coefficient models; variable selection; efficient estimation; quantile regression; linear-models; splines

摘要

This article considers high-dimensional image-on-scalar regression, where the spatial heterogeneity of covariate effects on imaging responses is investigated via a flexible partially linear spatially varying coefficient model. To tackle the challenges of spatial smoothing over the imaging response's complex domain consisting of regions of interest, we approximate the spatially varying coefficient functions via bivariate spline functions over triangulation. We first study estimation when the active constant coefficients and varying coefficient functions are known in advance. We then further develop a unified approach for simultaneous sparse learning and model structure identification in the presence of ultrahigh-dimensional covariates. Our method can identify zero, nonzero constant, and spatially varying components correctly and efficiently. The estimators of constant coefficients and varying coefficient functions are consistent and asymptotically normal for constant coefficient estimators. The method is evaluated by Monte Carlo simulation studies and applied to a dataset provided by the Alzheimer's Disease Neuroimaging Initiative.for this article are available online.