# huber.reg: Huber estimation for linear regression In MTE: Maximum Tangent Likelihood and Other Robust Estimation for High-Dimensional Regression

## Description

This function produces Huber estimates for linear regression. Initial estimates is required. Currently, the function does not support automatic selection of huber tuning parameter.

## Usage

 `1` ```huber.reg(y, X, beta.ini, alpha, intercept = FALSE) ```

## Arguments

 `y` the response vector `X` design matrix `beta.ini` initial value of estimates, could be from OLS. `alpha` 1/alpha is the huber tuning parameter delta. Larger alpha results in smaller portion of squared loss. `intercept` logical input that indicates if intercept needs to be estimated. Default is FALSE.

## Value

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

## 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.huber=huber.reg(y, X, beta0, 2, intercept=TRUE)\$beta cbind(c(-2,beta), beta.ls, beta.huber) ```

### Example output

```                  beta.ls beta.huber
(Intercept) -2 -0.8741926 -1.9042539
X1           1  1.8677738  0.9971322
X2          -1 -2.2162448 -1.0369297
X3           2 -0.7561486  1.9713509
X4          -2  1.2874911 -1.9702923
```

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