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

arXiv: https://arxiv.org/abs/1405.3379 · HTML: https://mlsanity.com/paper/1405.3379/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2014.

## Built on by (most cited first, 4 of 4)

- [HARFE: Hard-Ridge Random Feature Expansion](https://mlsanity.com/paper/2202.02877/) (2022)
- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)
- [Generalized Sparse Additive Model with Unknown Link Function](https://mlsanity.com/paper/2410.06012/) (2024)
- [Meta Additive Model: Interpretable Sparse Learning With Auto Weighting](https://mlsanity.com/paper/2604.20111/) (2026)

## Abstract (arXiv)

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.