The rate of convergence for sparse and low-rank quantile trace regression

Trace regression models are widely used in applications involving panel data, images, genomic microarrays, etc., where high dimensional covariates are often involved. However, the existing research involving high-dimensional covariates focuses mainly on the condition mean model. In this paper, we extend the trace regression model to the quantile trace regression model when the parameter is a matrix of simultaneously low rank and row (column) sparsity. The convergence rate of the penalized estimator is derived under mild conditions. Simulations, as well as a real data application, are also carried out for illustration.