huber.reg {MTE}

Huber estimation for linear 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

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

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)