# MTElasso: MTE-Lasso estimator In MTE: Maximum Tangent Likelihood and Other Robust Estimation for High-Dimensional Regression

## 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

 ```1 2``` ```MTElasso(y, X, beta.ini, p, lambda, adaptive = T, t, method = "MTE", intercept = FALSE, ...) ```

## Arguments

 `y` response vector. `X` design matrix, standardization is recommended. `beta.ini` initial estimates of beta. Using unpenalized MTE or LAD is recommended under high-dimensional setting. `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. `intercept` logical input that indicates if intercept needs to be estimated. Default is FALSE. `...` other arguments that are used in function "adalasso()" that is called form parcor package.

## 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 interatively updating coefficients.

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

## Examples

 ```1 2 3 4 5 6 7 8``` ```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)) beta0=MTE(y, X, rep(0,50), 0.1, 2)\$beta output.MTELasso=MTElasso(y,X, p=2, beta.ini=beta0, t=seq(0, 0.1, 0.01), method="MTE") beta.est=output.MTELasso\$beta ```

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