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

## Description

It estimates linear regression coefficient using MTE. The function produces robust estimates of linear regression. Outliers and contamination would be downweighted. It is robust to Gaussian assumption of the error term. Initial estimates need to be provided.

## Usage

 `1` ```MTE(y, X, beta.ini, t, p, intercept = FALSE) ```

## Arguments

 `y` the response vector `X` design matrix `beta.ini` initial value of estimates, could be from OLS. `t` the tangent point. You may specify a sequence of values, so that the function automatically select the optimal one. `p` Taylor expansion order, up to 3. `intercept` logical input that indicates if intercept needs to be estimated. Default is FALSE.

## Value

 `beta` the regression coefficient estimates `fitted.value` predicted response `t` the optimal tangent point through data-driven method

## Examples

 ```1 2 3 4 5 6 7 8``` ```set.seed(2017) n=200; d=4 X=matrix(rnorm(n*d), nrow=n, ncol=d) beta=c(1, -1, 2, -2) y=-2+X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100)) beta0=beta.ls=lm(y~X)\$coeff beta.MTE=MTE(y,X,beta0,0.1,2, intercept=TRUE)\$beta cbind(c(-2,beta), beta.ls, beta.MTE) ```

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