MTE: Maximum Tangent-likelihood Estimation

In MTE: Maximum Tangent Likelihood Estimation for Robust Linear Regression and Variable Selection

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 April 11, 2023, 6:11 p.m.