QICD (version 1.2.0)

QICD.BIC:

Description

Use the high dimensional BIC for quantile regression model on QICD algorithm, produces a plot and return a value for lambda

Usage

QICD.BIC(y, x, beta = NULL, const = 6, tau, lambda, 
a = 3.7, funname = "scad", intercept = TRUE, 
thresh = 1e-06, maxin = 100, maxout = 20, 
plot.off = F, ...)

Arguments

y

response y as in QICD.

x

x matrix as in QICD.

beta

beta vector as in QICD

const

a parameter to adjust the high dimensional BIC. A positive numerical value.

tau

tau value as in QICD

lambda

a user supplied lambda sequence. A numerical vector, which will be used as a pool for tuning parameter searching

a

a value as in QICD

funname

funname character vector as in QICD

intercept

intercept logical value as in QICD

thresh

thresh threshold as in QICD

maxin

maxin as in QICD

maxout

maxout as in QICD

plot.off

a logical value to control if a plot of QBIC vs. lambda will be produced. Default is FALSE and a plot will be given.

…

other argument that can be passed to plot

Value

an object of class "BIC.QICD" is returned, which is a list with the components of QBIC.

lambda

the values of lambda used in the fits.

HBIC

The high dimensional BIC is given-vector of length nlambda, as in QICD

nzero

number of non-zero coefficients at each lambda

lambda.min

value of lambda that gives minimum HBIC.

Details

The function run QICD nfolds times. For each specific lambda, the QBIC will be produced for comparison. Claim that cv.QICD does NOT search for values of a.

References

Peng,B and Wang,L. (2015)An Iterative Coordinate Descent Algorithm for High-dimensional Nonconvex Penalized Quantile Regression, Journal of Computational and Graphical Statistics http://amstat.tandfonline.com/doi/abs/10.1080/10618600.2014.913516 http://doi.org/10.1080/10618600.2014.913516 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

QICD,QICD.cv, QBIC

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.BIC=QICD.BIC(y, x, beta1,const=6, tau, 
lambda=seq(8,10,by=0.1), a,funname="scad",intercept=intercept)