Quantile regression with a total variation penalty was previously proposed due to its computational expediency as well as its local adaptiveness. However, the convergence rate of the method in this setting has been not rigorously established. In this short communication, we establish the convergence rate of O_p(n^−1/3) for the penalized estimator which is the same as in penalized least squares regression. Different from penalized least squares regression, in order to deal with the quantile loss function, we heavily rely on the Rademacher complexity of the class of functions of bounded variation.

中文翻译：

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非参数分位数回归的总收敛罚分的收敛速度

由于具有计算上的便利性和局部适应性，先前提出了具有总变化量罚分的分位数回归。但是，尚未严格确定该方法在这种情况下的收敛速度。在这段简短的交流中，我们为受罚估计量建立了O _p（n ^{1/3 1/3}）的收敛速度，这与受罚最小二乘回归中的收敛速度相同。与惩罚最小二乘回归不同，为了处理分位数损失函数，我们严重依赖有界变异函数类的Rademacher复杂度。