QICD.BIC: BIC for QICD on tuning parameter searching
In QICD: Estimate the Coefficients for Non-Convex Penalized Quantile Regression Model by using QICD Algorithm

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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, ...)

`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`

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.

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`.

Bo Peng

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

QICD,QICD.cv, QBIC

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)