L1pack: Routines for L1 estimation

L1pack provides routines to perform L1 estimation in linear regression models, estimation of mean and covariance matrix using the multivariate Laplace distribution, and multivariate random number generation for the Laplace distribution. A basic set of methods for printing the results is also available.

Currently, the L1pack provides support for the following R packages:

Resources

Latest binaries and sources can be found at the CRAN package repository:

• L1pack_0.62-4.tar.gz - Package sources
• L1pack_0.62-4.zip - Windows binaries (R-release)
• L1pack_0.62-4.tgz - MacOS binaries (R-release, arm64)
• L1pack_0.62-4.tgz - MacOS binaries (R-release, x86_64)

Reference Manual

• PDF manual | HTML manual

Installation

Install L1pack from CRAN using.

install.packages("L1pack")

You can install the latest development version from github with:

# install.packages("devtools")
# devtools::install_github("faosorios/L1pack")
install.packages("L1pack", repos = c('https://faosorios.r-universe.dev', 'https://cloud.r-project.org'))

Alternatively, you can download the source as a tarball or as a zip file. Unpack the tarball or zipfile (thereby creating a directory named, L1pack) and install the package source by executing (at the console prompt)

R CMD INSTALL L1pack

Next, you can load the package by using the command library(L1pack)

Methods

The methods implemented in L1pack include:

• Barrodale and Roberts (1974) procedure for L1 estimation in linear regression.
• EM algorithm for LAD estimation in linear regression (Phillips, 2002).
• Estimation of center and Scatter matrix using the multivariate Laplace distribution.
• Computation of L1 concordance correlation coefficient (Vallejos et al., 2025)
• Density, distribution function, quantile function and random number generation for univariate Laplace distribution.
• Density and random number generation for the multivariate Laplace distribution (Gomez et al., 1998).
• Computation of the generalized spatial median estimator as defined by Rao (1988)

Citation

To cite package L1pack in publications use:

citation("L1pack")
 
To cite package L1pack in publications use:
 
  Osorio, F., Wolodzko, T. (2026). Routines for L1 estimation. R
  package version 0.62-4. URL: https://github.com/faosorios/L1pack
 
A BibTeX entry for LaTeX users is
 
  @Manual{,
   title = {Routines for L1 estimation},
   author = {F. Osorio and T. Wolodzko},
   year = {2026},
   note = {R package version 0.62-4},
   url = {https://github.com/faosorios/L1pack},
  }

Papers using L1pack

• Osorio, F. (2026). On the mean-shift outlier model for LAD regression. Journal of Statistical Computation and Simulation, doi: 10.1080/00949655.2026.2716387
• Guest, L.M., McCabe, J., O'Halloran, C., Rana, M., Sun, W., Rudoler, D. (2024). Perspectives on work in the continuing care sector during and after the COVID-19 pandemic: A mixed-method design. Journal of Nursing Management, ID 7187263.
• Radojicic, U., Nordhausen, K. (2023). Least Absolute Value. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (Eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham.
• VandenHeuvel, D., Wu, J., Wang, Y.G. (2023). Robust regression for electricity demand forecast against cyberattacks. International Journal of Forecasting 39, 1573-1592.
• Plate, M., Bernstein, R., Hoppe, A., Bienefeld, K. (2019). Comparison of infinitesimal and finite locus models for long-term breeding simulations with direct and maternal effects at the example of honeybess. PLOS ONE 14, e0213270.
• Wang, W., Yu, P., Lin, L., Tong, T. (2019). Robust estimation of derivatives using locally weighted least absolute deviation regression. Journal of Machine Learning Research 20 (60), 1-49.

Providing Feedback

Please report any bugs/suggestions/improvements to Felipe Osorio. If you find these routines useful or not then please let me know. Also, acknowledgement of the use of the routines is appreciated.

About the Authors

Felipe Osorio is an applied statistician and creator of several R packages

• Webpage: faosorios.github.io

Tymoteusz Wolodzko is Software Engineer and Machine Learning Engineer. Also is elected moderator for CrossValidated.com

• Webpage: twolodzko.github.io