QR.mm {cqrReg}

Quantile Regression (QR) use Majorize and Minimize (mm) algorithm

Description

The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.

Usage

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

Arguments

X

the design matrix

y

response variable

tau

quantile level

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

References

David R.Hunter and Kenneth Lange. Quantile Regression via an MM Algorithm, Journal of Computational and Graphical Statistics, 9, Number 1, Page 60–77

Examples

set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
QR.mm(x,y,0.1)