Factorisable Multi-Task Quantile Regression∗

We propose a multivariate quantile regression framework that exploits the factor structure in multivariate conditional quantiles through nuclear norm regularization. Because the incurred optimization problem can only be solved approximately, we develop a non-asymptotic upper bound for the estimation error that takes into account the optimization error. We specify an algorithm to compute an approximate optimizer in the appendix. Merits of the proposed methodology are demonstrated through a Monte Carlo experiment and an application to financial study.