mmlasso: Robust and Sparse Estimators for Linear Regression Models

In esmucler/mmlasso: Robust and Sparse Estimators for Linear Regression Models

Description

Function to calculate the MM-Lasso and adaptive MM-Lasso estimators proposed in Smucler and Yohai (2015). The S-Ridge estimator of Maronna (2011) is used as the initial estimator.

Usage

mmlasso(x, y, varsigma=1, cualcv.mm=5, cualcv.S=5,
        numlam.mm=30, numlam.S=30, niter.S=50, niter.mm=50, ncores=1)

Arguments

x	A matrix of carriers. Intercept is added automatically.
y	A vector of response variables.
varsigma	Power to elevate the weights for the adaptive MM-Lasso. Default is 1.
cualcv.mm	A natural number greater than 2. Method for estimating prediction error of MM and adaptive MM-Lasso: cualcv-fold cross validation. Default is 5.
cualcv.S	A natural number greater than 2. Method for estimating prediction error of S-Ridge: cualcv-fold cross validation. Default is 5.
numlam.mm	Number of candidate penalization parameter values for MM and adaptive MM-Lasso. Default is 30.
numlam.S	Number of candidate penalization parameter values for S-Ridge. Default is 30.
niter.mm	Maximum number of weighted Lasso iterations for MM and adaptive MM-Lasso. Default is 50.
niter.S	Maximum number of iterations of IWLS for S-Ridge. Default is 50.
ncores	Number of cores to use for parallel computations. Default is one core.

Value

coef.SE	Initial S-Ridge estimate. First coordinate is the intercept.
coef.MMLasso	MM-Lasso estimate. First coordinate is the intercept.
coef.MMLasso.ad	adaptive MM-Lasso estimate. First coordinate is the intercept.

Author(s)

Ezequiel Smucler, [e-mail].

References

Ezequiel Smucler and Victor J. Yohai. Robust and sparse estimators for linear regression models (2015). Available at http://arxiv.org/abs/1508.01967.

Maronna, R.A. (2011). Robust Ridge Regression for High-Dimensional Data. Technometrics 53 44-53.

Examples

require(MASS)
p <- 8
n <- 60
rho <- 0.5
desv <- 1
beta.true <- c(rep(0,p+1))
beta.true[2] <- 3
beta.true[3] <- 1.5
beta.true[7] <- 2
mu <- rep(0,p)
sigma <- rho^t(sapply(1:p, function(i, j) abs(i-j), 1:p))
set.seed(1234)
x <- mvrnorm(n,mu,sigma)
u <- rnorm(n)*desv
y <- x%*%beta.true[2:(p+1)]+beta.true[1]+u

###Calculate estimators

set.seed(1234)
RobSparse <- mmlasso(x,y)

esmucler/mmlasso documentation built on May 16, 2019, 8:52 a.m.