QICD.BIC: BIC for QICD on tuning parameter searching

In geogria/QICD: Estimate the Coefficients for Non-Convex Penalized Quantile Regression Model by using QICD Algorithm

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

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.

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.

Author(s)

Bo Peng

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 doi: 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 doi: 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)

geogria/QICD documentation built on May 17, 2019, 1:12 a.m.