Multivariate quantile regression

2025-08-21

AI Summary

Existing multivariate quantile regression approaches—such as directional quantiles, vector quantiles, and copula-based methods—struggle to simultaneously ensure interpretability of conditional probability structures and flexibility in estimating marginal effects. This paper proposes a novel multivariate quantile regression framework grounded in the joint conditional distribution function. By sequentially applying univariate quantile regression, it constructs multivariate quantile curves that naturally embed conditional dependence structures, thereby enabling intuitive causal interpretation and modeling flexibility. We establish asymptotic properties theoretically; Monte Carlo simulations demonstrate robust finite-sample performance across diverse dependence configurations. An empirical application to exchange rate pass-through in Argentina (2004–2024) effectively captures dynamic multivariate risk. The core contribution lies in the first formal definition of multivariate quantiles directly anchored to the conditional distribution function—departing from conventional geometric or marginal distribution paradigms.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles, vector quantile regression, or copula-based methods--MQR defines quantiles through the conditional probability structure of the joint conditional distribution function. The method constructs multivariate quantile curves using sequential univariate quantile regressions derived from conditioning mechanisms, allowing for an intuitive interpretation and flexible estimation of marginal effects. The paper develops theoretical foundations of MQR, including asymptotic properties of the estimators. Through simulation exercises, the estimator demonstrates robust finite sample performance across different dependence structures. As an empirical application, the MQR framework is applied to the analysis of exchange rate pass-through in Argentina from 2004 to 2024.

Problem

• Develops multivariate quantile regression using conditional distribution functions
• Constructs quantile curves through sequential univariate regression conditioning
• Analyzes exchange rate pass-through in Argentina from 2004-2024

Innovation

• Multivariate quantile regression using conditional distribution function
• Sequential univariate quantile regressions from conditioning mechanisms
• Flexible estimation of marginal effects with intuitive interpretation