# Weighted-average quantile regression

arXiv: https://arxiv.org/abs/2203.03032 · HTML: https://mlsanity.com/paper/2203.03032/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 72 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Local Linear Forests](https://mlsanity.com/paper/1807.11408/) (2018)
- [Visually Communicating and Teaching Intuition for Influence Functions](https://mlsanity.com/paper/1810.03260/) (2018)
- [Extremal Quantile Regression: An Overview](https://mlsanity.com/paper/1612.06850/) (2016)
- [Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory](https://mlsanity.com/paper/1612.08099/) (2016)

## Abstract (arXiv)

In this paper, we introduce the weighted-average quantile regression framework, int01 qY|X(u)psi(u)du = X'β, where Y is a dependent variable, X is a vector of covariates, qY|X is the quantile function of the conditional distribution of Y given X, psi is a weighting function, and β is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters β. We show that our estimator is √ T-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where T is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.