QR.lasso.mm {cqrReg}

Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Majorize and Minimize (mm) algorithm

Description

The adaptive lasso parameter base on the estimated coefficient without penalty function. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.

Usage

QR.lasso.mm(X,y,tau,lambda,beta,maxit,toler)

Arguments

X

the design matrix.

y

response variable.

tau

quantile level.

lambda

The constant coefficient of penalty function. (default lambda=1)

beta

initial value of estimate coefficient.(default naive guess by least square estimation)

maxit

maxim iteration. (default 200)

toler

the tolerance critical for stop the algorithm. (default 1e-3)

Value

a list structure is with components

beta

the vector of estimated coefficient

b

intercept

Note

QR.lasso.mm(x,y,tau) work properly only if the least square estimation is good.

References

David R.Hunter and Runze Li.(2005) Variable Selection Using MM Algorithms,The Annals of Statistics 33, Number 4, Page 1617–1642.

Examples

set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements. 
QR.lasso.mm(x,y,0.1)