Risk bounds for quantile trend filtering
分位数趋势滤波的风险界
Summary We study quantile trend filtering, a recently proposed method for nonparametric quantile regression, with the goal of generalizing existing risk bounds for the usual trend-filtering estimators that perform mean regression. We study both the penalized and the constrained versions, of order $r \geqslant 1$, of univariate quantile trend filtering. Our results show that both the constrained and the penalized versions of order $r \geqslant 1$ attain the minimax rate up to…