g.ridge: An R Package for the Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

Abstract

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested by generalizing the uniform shrinkage of ridge regression to the non-uniform shrinkage, which was shown to perform well under sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (the first version published on 2023-12-07 at https://cran.r-project.org/package=g.ridge) that implements both the ridge estimator and generalized ridge estimators. The package equips with the generalized cross-validation for automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with the normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on “glmnet”, and hence, it can be the most recommended estimator under sparse and high-dimensional models. We demonstrate the package using the intracerebral hemorrhage data.