MTElasso: MTE-Lasso estimator

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

MTE-Lasso estimator

Description

MTELasso is the penalized MTE for robust estimation and variable selection for linear regression. It can deal with both fixed and high-dimensional settings.

Usage

MTElasso(
  X,
  y,
  beta.ini,
  p = 2,
  lambda = NULL,
  adaptive = TRUE,
  t = 0.01,
  intercept = TRUE,
  penalty.factor = rep(1, ncol(X)),
  ...
)

Arguments

X	design matrix, standardization is recommended.
y	response vector.
beta.ini	initial estimates of beta. If not specified, LADLasso estimates from rq.lasso.fit() in rqPen is used. Otherwise, robust estimators are strongly recommended.
p	Taylor expansion order.
lambda	regularization parameter for LASSO, but not necessary if "adaptive=TRUE".
adaptive	logic argument to indicate if Adaptive-Lasso is used. Default is TRUE.
t	the tuning parameter that controls for the tradeoff between robustness and efficiency. Default is t=0.01.
intercept	logical input that indicates if intercept needs to be estimated. Default is FALSE.
penalty.factor	can be used to force nonzero coefficients. Default is rep(1, ncol(X)) as in glmnet.
...	other arguments that are used in glmnet.

Value

It returns a sparse vector of estimates of linear regression. It has two types of penalty, LASSO and AdaLasso. Coordinate descent algorithm is used for iteratively updating coefficients.

beta	sparse regression coefficient
fitted	predicted response

Examples

set.seed(2017)
n=200; d=500
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, d-6))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.MTELasso=MTElasso(X, y, p=2, t=0.01)
beta.est=output.MTELasso$beta

MTE documentation built on April 11, 2023, 6:11 p.m.