The lasso for high dimensional regression with a possible change point

• 成果类型: Article
• 署名作者: Lee, Sokbae; Seo, Myung Hwan; Shin, Youngki
• 署名单位: Seoul National University (SNU); University of London; London School Economics & Political Science; University of London; London School Economics & Political Science; Western University (University of Western Ontario)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12108
• 发表日期: 2016
• 页码: 193-210
• 关键词: nonconcave penalized likelihood; quantile regression; variable selection; adaptive lasso; shrinkage; models; rates

摘要

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 l(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 factor that is nearly n(-1) 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.