A sensitivity analysis and error bounds for the adaptive lasso

Basu, Tathagata; Einbeck, Jochen; Troffaes, Matthias

Abstract

Sparse regression is an efficient statistical modelling technique which is of major relevance for high dimensional problems. There are several ways of achieving sparse regression, the well-known lasso being one of them. However, lasso variable selection may not be consistent in selecting the true sparse model. Zou (2006) proposed an adaptive form of the lasso which overcomes this issue, and showed that data driven weights on the penalty term will result in a consistent variable selection procedure. Weights can be informed by a prior execution of least squares or ridge regression. Using a power parameter on the weights, we carry out a sensitivity analysis for this parameter, and derive novel error bounds for the Adaptive lasso.

Citation

Basu, T., Einbeck, J., & Troffaes, M. (2020, December). A sensitivity analysis and error bounds for the adaptive lasso. Presented at International Workshop on Statistical Modelling, Bilbao

• Presentation Conference Type: Conference Paper (published)
• Conference Name: International Workshop on Statistical Modelling
• Acceptance Date: Jun 2, 2020
• Online Publication Date: Jul 20, 2020
• Publication Date: 2020
• Deposit Date: Oct 1, 2020
• Publicly Available Date: Oct 8, 2020
• Publisher: Universidad del Pais Vasco
• Pages: 278-281
• Book Title: Proceedings of the 35th International Workshop on Statistical Modelling.
• Public URL: https://durham-repository.worktribe.com/output/1141665
• Publisher URL: https://web-argitalpena.adm.ehu.es/pdf/USPDF202673.pdf