Regularized Tensor Quantile Regression With Applications to Neuroimaging Data Analysis

This article proposes a regularized linear quantile regression model with a scalar response and tensor-valued covariates. Our model uniquely regularizes the parameters of a low-dimensional tensor effect decomposition through the tensor estimate rather than directly through the decomposition's parameters. We establish the computational and statistical properties of the proposed algorithm and estimators, both of which require separate treatment due to the quantile loss function. Simulation studies demonstrate the superiority of our model over existing tensor frameworks when traditional regression assumptions are violated. A real-world neuroimaging analysis further highlights the interpretability benefits of our approach.