QR.lasso.mm {cqrReg} | R Documentation |
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.
QR.lasso.mm(X,y,tau,lambda,beta,maxit,toler)
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) |
a list
structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
QR.lasso.mm(x,y,tau) work properly only if the least square estimation is good.
David R.Hunter and Runze Li.(2005) Variable Selection Using MM Algorithms,The Annals of Statistics 33, Number 4, Page 1617–1642.
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)