Expectile trace regression via low-rank and group sparsity regularization

Trace regression has received a lot of attention due to its ability to account for matrix-type covariates, including panel data, images, and genomic microarrays as special cases. However, most of its existing research focuses on the case of mean regression. In this paper, we consider the expectile trace regression, which can provide a more diversified picture of the regression relationship at different expectiles, via the low-rank and group sparsity regularization. The upper bound for the statistical rate of convergence of the regularized estimator is established under some mild conditions. Some simulations, as well as a real data example, are also provided to illustrate the finite sample performance of the developed expectile trace regression.