cqr.lasso.cd {cqrReg}

Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Coordinate Descent (cd) Algorithms

Description

The adaptive lasso parameter base on the estimated coefficient without penalty function. Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.

Usage

cqr.lasso.cd(X,y,tau,lambda,beta,maxit,toler)

Arguments

X

the design matrix

y

response variable

tau

vector of 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

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

References

Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, 2, No 1, 224–244.

Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.

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)
tau=1:5/6
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements. 
cqr.lasso.cd(x,y,tau)