MTE (version 1.0.0)

MTElasso: 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(y, X, beta.ini, p, lambda, adaptive = T, t, method = "MTE",
  intercept = FALSE, ...)

Arguments

y

response vector.

X

design matrix, standardization is recommended.

beta.ini

initial estimates of beta. Using unpenalized MTE or LAD is recommended under high-dimensional setting.

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 tangent point. You may specify a sequence of values, so that the function automatically select the optimal one.

method

it can be ("MTE", "MLE"). The default is MTE.

intercept

logical input that indicates if intercept needs to be estimated. Default is FALSE.

...

other arguments that are used in function "adalasso()" that is called form parcor package.

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 interatively updating coefficients.

beta

sparse regression coefficient

fitted

predicted response

t

optimal tangent point

Examples

# NOT RUN {
set.seed(2017)
n=200; d=50
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, 44))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
beta0=MTE(y, X, rep(0,50), 0.1, 2)$beta
output.MTELasso=MTElasso(y,X, p=2, beta.ini=beta0, t=seq(0, 0.1, 0.01), method="MTE")
beta.est=output.MTELasso$beta

# }