Prediction error bounds for linear regression with the TREX Academic Article

abstract

• 2018, Sociedad de Estadstica e Investigacin Operativa. The TREX is a recently introduced approach to sparse linear regression. In contrast to most well-known approaches to penalized regression, the TREX can be formulated without the use of tuning parameters. In this paper, we establish the first known prediction error bounds for the TREX. Additionally, we introduce extensions of the TREX to a more general class of penalties, and we provide a bound on the prediction error in this generalized setting. These results deepen the understanding of the TREX from a theoretical perspective and provide new insights into penalized regression in general.

authors

• Gaynanova, Irina

published proceedings

• TEST

author list (cited authors)

• Bien, J., Gaynanova, I., Lederer, J., & Mueller, C. L.

citation count

• 11

complete list of authors

• Bien, Jacob||Gaynanova, Irina||Lederer, Johannes||Mueller, Christian L

publication date

• June 2019

publisher

• Springer Nature  Publisher

published in

• Test  Journal

keywords

• High-dimensional Regression
• Oracle Inequalities
• Trex
• Tuning Parameters

Digital Object Identifier (DOI)

• 10.1007/s11749-018-0584-4

start page

• 451

end page

• 474

volume

• 28

issue

• 2

URL

• http://dx.doi.org/10.1007/s11749-018-0584-4