We consider both ℓ0-penalized and ℓ0-constrained quantile regression estimators. For the estimator, we derive an exponential inequality on tail probability of excess prediction risk apply it to obtain non-asymptotic upper bounds mean-square parameter function estimation errors. also analogous results for estimator. The resulting rates convergence are nearly minimax-optimal same as those ℓ1-pena...

Abstract Regular variation provides a convenient theoretical framework for studying large events. In the multivariate setting, spectral measure characterizes dependence structure of extremes. This gathers information on localization extreme events and often has sparse support since severe do not simultaneously occur in all directions. However, it is defined through weak convergence, which does ...