# 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

 ```1 2``` ```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, [email protected].

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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 Oct. 31, 2017, 10:55 a.m.