# MTE: Maximum Tangent-likelihood Estimation In MTE: Maximum Tangent Likelihood Estimation for Linear Regression

 MTE R Documentation

## Maximum Tangent-likelihood Estimation

### 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

```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

Returns estimates from MTE method.

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

### Examples

```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 March 23, 2022, 1:07 a.m.