smoothedLasso (version 1.6)

standardLasso: Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso.

Description

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso.

Usage

standardLasso(X, y, lambda)

Arguments

X

The design matrix.

y

The response vector.

lambda

The Lasso regularization parameter.

Value

A list with six functions, precisely the objective \(u\), penalty \(v\), and dependence structure \(w\), as well as their derivatives \(du\), \(dv\), and \(dw\).

References

Tibshirani, R. (1996). Regression Shrinkage and Selection Via the Lasso. J Roy Stat Soc B Met, 58(1):267-288.

Hahn, G., Lutz, S., Laha, N., and Lange, C. (2020). A framework to efficiently smooth L1 penalties for linear regression. bioRxiv:2020.09.17.301788.

Examples

# NOT RUN {
library(smoothedLasso)
n <- 100
p <- 500
betavector <- runif(p)
X <- matrix(runif(n*p),nrow=n,ncol=p)
y <- X %*% betavector
lambda <- 1
temp <- standardLasso(X,y,lambda)

# }