Associate Professor of Statistics
“Spatial Quantile Regression Models for High-Dimensional Imaging Data”
The aim of this paper is to develop a spatial quantile regression framework for accurately quantifying high-dimensional image data conditional on some scalar predictors. This new framework allows us to delineate spatial quantile association between neuroimaging data and covariates, while explicitly modeling spatial dependence in neuroimaging data. Theoretically, we establish the minimax rates of convergence for the prediction risk under both fixed and random designs. We further develop efficient algorithms such as the ADMM and the primal-dual algorithm to estimate the varying coefficients. Our method is able to estimate the whole conditional distribution of the image response given the scalar covariates. Simulations and real data analysis are conducted to examine the finite-sample performance.
This is a joint work with Zhengwu Zhang, Linglong Kong, and Hongtu Zhu.