Maximum Tangent Likelihood Estimation for Robust Linear Regression and Variable Selection

Several robust estimators for linear regression and variable selection are provided. Included are Maximum tangent likelihood estimator by Qin, et al., (2017), arXiv preprint , least absolute deviance estimator and Huber regression. The penalized version of each of these estimator incorporates L1 penalty function, i.e., LASSO and Adaptive Lasso. They are able to produce consistent estimates for both fixed and high-dimensional settings.

MTE: Maximum Tangent Likelihood Estimation

Overview

The package provides several robust estimation methods for linear regression under both fixed and high dimesional settings. The methods include Maximum Tangent Likelihood Estimator (MTE and MTElasso) (Qin et al., 2017+), Least Absolute Deviance Estimator (LAD and LADlasso) and Huber estimator (huber.reg and huber.lasso).

Installation

devtools::install_github("shaobo-li/MTE")

Example

library(MTE)
set.seed(2017)
n=200; d=500
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, d-6))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.MTELasso=MTElasso(X, y, p=2, t=0.01)
beta.est=output.MTELasso$beta

References

Qin, Y., Li, S., Li, Y., & Yu, Y. (2017). Penalized maximum tangent likelihood estimation and robust variable selection. doi:10.48550/arXiv.1708.05439.