QICD (version 1.2.0)

QBIC:

Description

A high dimensional BIC will be returned specificall for quantile regression

Usage

QBIC(y, X, beta, tau = 0.5, const = 6)

Arguments

y

response y as in QICD.

X

x matrix as in QICD.

beta

the coefficients vector for BIC calculation

tau

tau value as in QICD

const

a constant to adjust the BIC. A positive numerical value; default value is 6.

Value

QBIC will be returned, which is a numerical value

Details

The high dimensional BIC for quantile regression model is $$log(checkloss)+|S|log(log(n))C_n/n$$ where S is the selected model in QICD, n is the number of obs, C_n is some positive constant which diverges to infinity as n increases. Actually, C_n is log(p)/const.

References

Lee, E. R., Noh, H. and Park. B. (2013) Model Selection via Bayesian Information Criterion for Quantile Regression Models. Journal of the American Statistical Associa- tion, preprint. http://www.tandfonline.com/doi/pdf/10.1080/01621459.2013.836975 http://doi.org/10.1080/01621459.2013.836975 Wang,L., Kim, Y., and Li,R. (2013+) Calibrating non-convex penalized regression in ultra-high dimension. To appear in Annals of Statistics. http://users.stat.umn.edu/~wangx346/research/nonconvex.pdf

See Also

checkloss, QICD

Examples

x=matrix(rnorm(1000),50)
n=dim(x)[1]
p=dim(x)[2]
intercept=1
y=x[,1]+x[,7]+x[,9]+0.1*rnorm(n)
beta1=rep(0,p+intercept)
tau=0.5
a=2.7
res=QICD(y,x,beta1,tau,lambda=10,a,"scad",intercept=intercept)
QBIC(y,cbind(x,rep(1,n)),res$beta_final,tau=tau)