# Expectile Asymptotics

arXiv: https://arxiv.org/abs/1509.06866 · HTML: https://mlsanity.com/paper/1509.06866/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Distributional Reinforcement Learning with Dual Expectile-Quantile Regression](https://mlsanity.com/paper/2305.16877/) (2023)
- [Limit Theory for Online Expectile Estimation under Short and Long Range Dependence](https://mlsanity.com/paper/2610.16030/) (2026)

## Abstract (arXiv)

We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the additional assumption of continuity of the distribution function at the expectile implies asymptotic normality, otherwise, the limit is non-normal. For a continuous distribution function we show the uniform central limit theorem for the expectile process. If, in contrast, the distribution is heavy-tailed, and contained in the domain of attraction of a stable law with 1 < α < 2, then we show that the expectile is also asymptotically stable distributed. Our findings are illustrated in a simulation section.