Quantile trace regression via nuclear norm regularization

Abstract Trace regression models are widely used to accommodate matrix-type covariates, such as panel data, images, genomics microarrays, etc. In this paper, we extend the trace regression to the quantile trace regression model. The optimal convergence rate of the estimator is derived under mild conditions. Some simulations are carried out for illustration. Finally, we apply the proposed method to a students’ behavior data set related to personalized education.