Model selection by LASSO methods in a change-point model

TL;DR

This paper investigates the use of LASSO and adaptive LASSO methods for simultaneous change-point detection and variable selection in linear regression models, establishing their asymptotic properties and demonstrating their effectiveness through numerical examples.

Contribution

It introduces a model selection criterion for LASSO-based change-point models and proves the oracle properties of the adaptive LASSO estimator in this context.

Findings

Adaptive LASSO outperforms LS in variable selection.

Oracle properties are established for adaptive LASSO estimators.

Numerical examples confirm the effectiveness of the proposed methods.

Abstract

The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows the parametric estimation, including the change-points, and automatic variable selection simultaneously. The asymptotic properties of the LASSO-type (which has as particular case the LASSO estimator) and of the adaptive LASSO estimators are studied. For this last estimator the oracle properties are proved. In both cases, a model selection criterion is proposed. Numerical examples are provided showing the performances of the adaptive LASSO estimator compared to the LS estimator.