dlasso {DLASSO} R Documentation

## An implementation of dlasso using iterative ridge algorithm

### Description

This function allows implementing differentiable lasso (dlasso) for arbitrary values of λ and s.

### Usage

```dlasso (x,
y,
s  =  1           ,
intercept = FALSE ,
c  = 1            ,
lambda = NULL     ,
split  = 50       ,
maxIter = 500     ,
lowlambda = 10^-3 ,
digit = 5         ,
cauchy = FALSE    ,
force = 'auto'    ,
trace = FALSE)
```

### Arguments

 `x` Matrix of predictors `y` Response vector `s` A single or a vector of precision value, s, given adp=FALSE. Default is 1. See "adp" parameter. `intercept` Logical flag. If TRUE, an intercept is included in the model, otherwise no intercept is included. Default is FALSE. `c` Choose between dlasso (c=1) and dSCAD (c=-1). Default is dlasso. See futher "force" parameter. `adp` Logical flag. TRUE to use adaptive adjustment for s. If TRUE then the function ignores the initial s. `lambda` Optional values for the tuning parameter. A single value or a sequence of values. Useful for manually searching over user defined set of tuning values. Set to any negative value to activate the automatic setting for λ.max and λ.min. `split` The number of splits between λ.min and λ.max. `maxIter` The maximum iterations for the algorithm. Default is 500. `adj` Positive value. This value adjusts the upper value for the penalty term, adj*λ.max. `lowlambda` The lower limit for the tuning parameter. Default is 10^-3. `digit` The maximum number of digits before setting an estimation to zero. The default is 5 digits. `cauchy` Logical flag. Set to TRUE to use Cauchy CDF instead of Gaussian one in the penalty function. The default is Gaussian. `force` Logical flag. Set to TRUE to let only a decrease in absolute estimation of the parameters. Default is 'auto' that is only applied if sqrt(n)>2*log(p) for n the number of observations and p the number of parameters. `trace` Logical flag. If TRUE, output contains some information about the steps. Default is FALSE.

### Value

A "dlasso" object of the form of a matrix ( λ | s | AICc | GIC | BIC | GCV | estimations).

### Author(s)

`coef.dlasso`,`plot.dlasso`

### Examples

```    # dLASSO
r = 5
zr= 95
n = 50
b = c(1:r,rep(0,zr))
x = matrix(rnorm((r+zr)*n),ncol=r+zr)
y = x %*% b +rnorm(n)