Factor Augmented Quantile Regression Model

TL;DR

This paper introduces a factor-augmented quantile regression framework that effectively handles high-dimensional data with complex dependencies, heavy tails, and mixed sparse and dense effects, combining robustness, efficiency, and theoretical guarantees.

Contribution

The paper proposes a novel FAQR method integrating factor analysis with quantile regression, including convolution smoothing for improved computation and theoretical validation.

Findings

Accurate factor selection and parameter estimation demonstrated.

Effective in heavy-tailed noise scenarios like t-distributions.

Bootstrap diagnostic procedure assesses model adequacy.

Abstract

Along with the widespread adoption of high-dimensional data, traditional statistical methods face significant challenges in handling problems with high correlation of variables, heavy-tailed distribution, and coexistence of sparse and dense effects. In this paper, we propose a factor-augmented quantile regression (FAQR) framework to address these challenges simultaneously within a unified framework. The proposed FAQR combines the robustness of quantile regression and the ability of factor analysis to effectively capture dependencies among high-dimensional covariates, and also provides a framework to capture dense effects (through common factors) and sparse effects (through idiosyncratic components) of the covariates. To overcome the lack of smoothness of the quantile loss function, convolution smoothing is introduced, which not only improves computational efficiency but also eases theoretical derivation. Theoretical analysis establishes the accuracy of factor selection and consistency in parameter estimation under mild regularity conditions. Furthermore, we develop a Bootstrap-based diagnostic procedure to assess the adequacy of the factor model. Simulation experiments verify the rationality of FAQR in different noise scenarios such as normal and $t_2$ distributions.