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Main Authors: Jiang, Rong, Jones, M. C., Yu, Keming, Wang, Jiangfeng
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2506.23059
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author Jiang, Rong
Jones, M. C.
Yu, Keming
Wang, Jiangfeng
author_facet Jiang, Rong
Jones, M. C.
Yu, Keming
Wang, Jiangfeng
contents Regression models that go beyond the mean, alongside coherent risk measures, have been important tools in modern data analysis. This paper introduces the innovative concept of Average Quantile Regression (AQR), which is smooth at the quantile-like level, comonotonically additive, and explicitly accounts for the severity of tail losses relative to quantile regression. AQR serves as a versatile regression model capable of describing distributional information across all positions, akin to quantile regression, yet offering enhanced interpretability compared to expectiles. Numerous traditional regression models and coherent risk measures can be regarded as special cases of AQR. As a flexible non-parametric regression model, AQR demonstrates outstanding performance in analyzing high-dimensional and large datasets, particularly those generated by distributed systems, and provides a convenient framework for their statistical analysis. The corresponding estimators are rigorously derived, and their asymptotic properties are thoroughly developed. In a risk management context, the case study confirms AQR's effectiveness in risk assessment and portfolio optimization.
format Preprint
id arxiv_https___arxiv_org_abs_2506_23059
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Average quantile regression: a new non-mean regression model and coherent risk measure
Jiang, Rong
Jones, M. C.
Yu, Keming
Wang, Jiangfeng
Statistics Theory
Regression models that go beyond the mean, alongside coherent risk measures, have been important tools in modern data analysis. This paper introduces the innovative concept of Average Quantile Regression (AQR), which is smooth at the quantile-like level, comonotonically additive, and explicitly accounts for the severity of tail losses relative to quantile regression. AQR serves as a versatile regression model capable of describing distributional information across all positions, akin to quantile regression, yet offering enhanced interpretability compared to expectiles. Numerous traditional regression models and coherent risk measures can be regarded as special cases of AQR. As a flexible non-parametric regression model, AQR demonstrates outstanding performance in analyzing high-dimensional and large datasets, particularly those generated by distributed systems, and provides a convenient framework for their statistical analysis. The corresponding estimators are rigorously derived, and their asymptotic properties are thoroughly developed. In a risk management context, the case study confirms AQR's effectiveness in risk assessment and portfolio optimization.
title Average quantile regression: a new non-mean regression model and coherent risk measure
topic Statistics Theory
url https://arxiv.org/abs/2506.23059