Learning rates for the risk of kernel based quantile regression estimators in additive models

TL;DR

This paper establishes learning rates for kernel-based additive models in semiparametric statistics, showing advantages in high-dimensional settings and providing a specific example of kernel space inclusion.

Contribution

It provides new learning rates for regularized kernel methods in additive models, highlighting benefits over non-additive approaches in high dimensions.

Findings

Favorable learning rates in high-dimensional additive models

Additive Gaussian kernels include certain univariate Gaussian functions

Comparison with non-additive Gaussian kernel spaces

Abstract

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.