# Learning Rates for Kernel-Based Expectile Regression

## TL;DR

This paper analyzes a support vector machine approach for estimating conditional expectiles, establishing minimax optimal learning rates with Gaussian RBF kernels, improving upon previous kernel regression results.

## Contribution

It introduces a new analysis of kernel-based expectile regression with optimal learning rates, leveraging advanced entropy bounds and calibration inequalities.

## Key findings

- Achieves minimax optimal learning rates for kernel expectile regression.
- Improves existing rates for kernel-based least squares regression.
- Provides new theoretical tools for analyzing asymmetric loss functions.

## Abstract

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are used and the desired expectile is smooth in a Besov sense. As a special case, our learning rates improve the best known rates for kernel-based least squares regression in this scenario. Key ingredients of our statistical analysis are a general calibration inequality for the asymmetric least squares loss, a corresponding variance bound as well as an improved entropy number bound for Gaussian RBF kernels.