huber.lasso: Huber-Lasso estimator

In MTE: Maximum Tangent Likelihood and Other Robust Estimation for High-Dimensional Regression

Description

This function is L1 penalized Huber estimator for linear regression under both fixed and high-dimensional settings. Currently, the function does not support automatic selection of huber tuning parameter.

Usage

huber.lasso(y, X, beta.ini, lambda, alpha = 2, adaptive = T,
  intercept = FALSE)

Arguments

y	response vector.
X	design matrix, standardization is recommended.
beta.ini	initial estimates of beta. Using unpenalized Huber or LAD is recommended under high-dimensional setting.
lambda	regularization parameter of Lasso or adaptive Lasso (if adaptive=TRUE).
alpha	1/alpha is the huber tuning parameter. Larger alpha results in smaller portion of squared loss.
adaptive	logical input that indicates if adaptive Lasso is used. Default is TRUE.
intercept	logical input that indicates if intercept needs to be estimated. Default is FALSE.

Value

beta	the regression coefficient estimates.
fitted	predicted response.
iter.steps	iteration steps.

Examples

set.seed(2017)
n=200; d=50
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, 44))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.HuberLasso=huber.lasso(y,X, beta.ini=LAD(y, X), lambda=0.2, adaptive=TRUE)
beta.est=output.HuberLasso$beta

MTE documentation built on May 2, 2019, 5:57 a.m.