Prediction error bounds for linear regression with the TREX

• Jacob Bien ^[1] ; Irina Gaynanova ^[2] ; Johannes Lederer ^[3] ; Christian L. Müller ^[4]
  1. [1] University of Southern California

     University of Southern California

     Estados Unidos

     
  2. [2] Texas A&M University

     Texas A&M University

     Estados Unidos

     
  3. [3] University of Washington

     University of Washington

     Estados Unidos

     
  4. [4] Simons Foundation

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 2, 2019, págs. 451-474
• Idioma: inglés
• DOI: 10.1007/s11749-018-0584-4
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.