# MTElasso: MTE-Lasso estimator In MTE: Maximum Tangent Likelihood Estimation for Linear Regression

 MTElasso R Documentation

## MTE-Lasso estimator

### Description

MTELasso is the penalized MTE for robust estimation and variable selection for linear regression. It can deal with both fixed and high-dimensional settings.

### Usage

```MTElasso(
X,
y,
beta.ini,
p,
lambda,
t,
method = "MTE",
intercept = FALSE,
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. `p` Taylor expansion order. `lambda` regularization parameter for LASSO, but not necessary if "adaptive=TRUE". `adaptive` logic argument to indicate if Adaptive-Lasso is used. Default is TRUE. `t` the tangent point. You may specify a sequence of values, so that the function automatically select the optimal one. `method` it can be ("MTE", "MLE"). The default is MTE. If MLE, classical LASSO is used. `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. `...` other arguments that are used in `glmnet`.

### Value

It returns a sparse vector of estimates of linear regression. It has two types of penalty, LASSO and AdaLasso. Coordinate descent algorithm is used for iteratively updating coefficients.

 `beta` sparse regression coefficient `fitted` predicted response `t` optimal tangent point

### 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.MTELasso=MTElasso(X, y, p=2, t=0.05, method="MTE")
beta.est=output.MTELasso\$beta

```

MTE documentation built on March 23, 2022, 1:07 a.m.