This R package provides tools for estimating a quantile regression model with a penalized objective function. Implements a variety of penalties, including group penalties.
For most up to date versions use the following code. However, be warned the github package is often in a state of testing and debugging.
devtools::install_github("bssherwood/rqpen")library(rqPen)
n<- 200
p<- 30
x0<- matrix(rnorm(n*p),n,p)
X<- cbind(x0, x0^2, x0^3)[,order(rep(1:p,3))]
y<- -2+X[,1]+0.5*X[,2]-X[,3]-0.5*X[,7]+X[,8]-0.2*X[,9]+rt(n,2)
group<- rep(1:p, each=3)
# lasso estimation
# one tau
fit1 <- rq.pen(x,y)
# several values of tau
fit2 <- rq.pen(x,y,tau=c(.2,.5,.8))
# Group SCAD estimation
fit3 <- rq.group.pen(x,y,groups=group,penalty="gSCAD")
# cross validation
cv1 <- rq.pen.cv(x,y)
plot(cv1)
cv2 <- rq.pen.cv(x,y,tau=c(.2,.5,.8))
plot(cv2)
cv3 <- rq.group.pen(x,y,groups=group,penalty="gSCAD")
plot(cv3)
# BIC selection of tuning parameters
qs1 <- qic.select(fit1)
qs2 <- qic.select(fit2)
qs3 <- qic.select(fit3)Sherwood, B. and Li, S. (2021) An Efficient Approach to Feature Selection and Estimation for Quantile Regression with Grouped Variables, Working paper.