Regression Coefficients Estimation Using the Generalized Cross Entropy

Estimation and inference using the Generalized Maximum Entropy (GME) and Generalized Cross Entropy (GCE) framework, a flexible method for solving ill-posed inverse problems and parameter estimation under uncertainty (Golan, Judge, and Miller (1996, ISBN:978-0471145925) "Maximum Entropy Econometrics: Robust Estimation with Limited Data"). The package includes routines for generalized cross entropy estimation of linear models including the implementation of a GME-GCE two steps approach. Diagnostic tools, and options to incorporate prior information through support and prior distributions are available (Macedo, Cabral, Afreixo, Macedo and Angelelli (2025) ). In particular, support spaces can be defined by the user or be internally computed based on the ridge trace or on the distribution of standardized regression coefficients. Different optimization methods for the objective function can be used. An adaptation of the normalized entropy aggregation (Macedo and Costa (2019) "Normalized entropy aggregation for inhomogeneous large-scale data") and a two-stage maximum entropy approach for time series regression (Macedo (2022) ) are also available. Suitable for applications in econometrics, health, signal processing, and other fields requiring robust estimation under data constraints.

GCE

GCEstim: Generalized Cross Entropy linear models in R.

Recent/release notes

• Major updates.

Features

• Estimates linear regression coefficients using Generalized Cross Entropy.

Overview

GCEstim provides tools for estimating linear regression models using Generalized Cross Entropy (GCE) and related information-theoretic estimators. The package is particularly useful in situations involving multicollinearity, small sample sizes, ill-conditioned design matrices, or when prior information is available.

The package includes estimation, model selection, support-space construction, cross-validation, bootstrap inference, and diagnostic tools.

Examples

res.lmgce.v01 <-
  lmgce(
    formula = y ~ X001 + X002 + X003 + X004,
    data = dataThesis,
    boot.B = 100,
    boot.method = "residuals")

summary(res.lmgce.v01)
plot(res.lmgce.v01)

Installation

• Development version from Github:

devtools::install_github("jorgevazcabral/GCEstim",
                         build_vignettes = TRUE,
                         build_manual = TRUE,
                         dependencies=TRUE)

• Stable version from CRAN:

install.packages("GCEstim")

Development Status

GCEstim is under active development. Bug reports, feature requests, and pull requests are welcome through GitHub Issues.

Links

• CRAN: https://cran.r-project.org/package=GCEstim
• GitHub: https://github.com/jorgevazcabral/GCEstim
• Issues: https://github.com/jorgevazcabral/GCEstim/issues

References

Golan, Judge and Miller (1996). Maximum Entropy Econometrics.

Golan (2018). Foundations of Info-Metrics.

Cabral et al. (2025). GCEstim: Regression Coefficients Estimation Using the Generalized Cross Entropy.

Citation

In case you want / have to cite this package, please use citation('GCEstim') for citation information.