Learning rates for the risk of kernel based quantile regression estimators in additive models
This work provides theoretical guarantees for quantile regression in additive models, which is incremental but useful for high-dimensional statistical applications.
The paper establishes learning rates for kernel-based quantile regression estimators in additive models, showing that these rates compare favorably to nonparametric kernel methods in high dimensions when the additive assumption holds.
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.