Prediction error bounds for linear regression with the TREX

Jacob Bien, Irina Gaynanova, Johannes Lederer () and Christian L. Müller
Additional contact information
Jacob Bien: University of Southern California
Irina Gaynanova: Texas A&M University
Johannes Lederer: University of Washington
Christian L. Müller: Simons Foundation

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 2, No 15, 474 pages

Abstract: Abstract 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.

Keywords: TREX; High-dimensional regression; Tuning parameters; Oracle inequalities; 62J07 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11749-018-0584-4

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