We introduce a user-friendly computational framework for implementing robust versions of a wide variety of structured regression methods with the L2 criterion. In addition to introducing an algorithm for performing L2E regression, our framework enables robust regression with the L2 criterion for additional structural constraints, works without requiring complex tuning procedures on the precision parameter, can be used to identify heterogeneous subpopulations, and can incorporate readily available non-robust structured regression solvers. We provide convergence guarantees for the framework and demonstrate its flexibility with some examples. Supplementary materials for this article are available online.


To install the latest stable version from CRAN:


To install the latest development version from GitHub:

# install.packages("devtools")

Getting Started

We’ve included an introductory demo on how to use the L2E framework with examples from the accompanying journal manuscript.

Citing L2E

The accompanying journal manuscript for L2E can be found at arXiv:2105.03228 and at the Journal of Computational and Graphical Statistics. To cite the L2E framework, please use the following BibTeX entry.

  author = {Jocelyn T. Chi and Eric C. Chi},
  title = {A User-Friendly Computational Framework for Robust Structured Regression with the L$_2$ Criterion},
  journal = {Journal of Computational and Graphical Statistics, In press.},
  year = {2022},
  url = {https://amstat.tandfonline.com/doi/full/10.1080/10618600.2022.2035232#.Yfr47S-B0Ts},
  doi = {10.1080/10618600.2022.2035232},