Quantile regression in high-dimension with breaking

TL;DR

This paper develops robust quantile regression methods with penalties for high-dimensional change-point models, effectively estimating parameters and change-points even with heavy-tailed errors.

Contribution

It introduces penalized quantile regression techniques that maintain oracle properties in high-dimensional change-point models with heavy-tailed errors.

Findings

Methods achieve consistent change-point and parameter estimation.

Convergence rates are established for both estimators.

Simulations demonstrate effective performance of the proposed methods.

Abstract

The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed errors is considered. In this case, least square method with LASSO or adaptive LASSO penalty can not be used since the theoretical assumptions do not occur or the estimators are not robust. Then, the quantile model with SCAD penalty or median regression with LASSO-type penalty allows, in the same time, to estimate the parameters on every segment and eliminate the irrelevant variables. We show that, for the two penalized estimation methods, the oracle properties is not affected by the change-point estimation. Convergence rates of the estimators for the change-points and for the regression parameters, by the two methods are found. Monte-Carlo simulations illustrate the performance of the methods.