# huber.lasso: Huber-Lasso estimator In MTE: Maximum Tangent Likelihood Estimation for Robust Linear Regression and Variable Selection

 huber.lasso R Documentation

## Huber-Lasso estimator

### 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(
X,
y,
beta.ini,
lambda,
alpha = 2,
intercept = TRUE,
penalty.factor = rep(1, ncol(X))
)
``````

### Arguments

 `X` design matrix, standardization is recommended. `y` response vector. `beta.ini` initial estimates of beta. If not specified, LADLasso estimates from `rq.lasso.fit()` in `rqPen` is used. Otherwise, robust estimators are strongly recommended. `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. `penalty.factor` can be used to force nonzero coefficients. Default is rep(1, ncol(X)) as in glmnet.

### Value

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

### Examples

``````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.HuberLasso=huber.lasso(X,y)
beta.est=output.HuberLasso\$beta

``````

MTE documentation built on April 11, 2023, 6:11 p.m.