The Lasso for High-Dimensional Regression with a Possible Change-Point

Abstract

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the ${\ell }_1$ estimation loss for regression coefficients. Since the Lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a nearly $n^{-1}$ factor even when the number of regressors can be much larger than the sample size ($n$). We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data.

References in corpus (6)

• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• Lasso-type recovery of sparse representations for high-dimensional data
• High-dimensional generalized linear models and the lasso
• Sparsity oracle inequalities for the Lasso
• High-Dimensional Sparse Additive Hazards Regression
• Non-Concave Penalized Likelihood with NP-Dimensionality

Cited by in corpus (8)

• Estimation of Dynamic Panel Threshold Model using Stata
• Oracle Estimation of a Change Point in High Dimensional Quantile Regression
• Computationally efficient change point detection for high-dimensional regression
• Adaptive LASSO model selection in a multiphase quantile regression
• Detection and inference of changes in high-dimensional linear regression with non-sparse structures
• Post Selection Shrinkage Estimation for High Dimensional Data Analysis
• Online jump and kink detection in segmented linear regression: Statistical optimality meets computational efficiency
• Structural Change in Sparsity