MTElasso {MTE}

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