QICD (version 1.2.0)

QICD-package:

Description

Estimation of coefficients of nonconvex penalized quantile regression model by using the Iterative Coordinate Descent (QICD) algorithm. This algorithm relies on a tuning parameter lambda that will be chosen by both k-fold cross validation and high dimensional BIC for quantile regression model.

Details

Package:	QICD
Type:	Package
Version:	1.2
Date:	2017-04-16
License:	GPL-2

This is a package to utilize the QICD algorithm on penalized quantile regression. Accepts x,y, lambda as predictor matrix, response variable and tuning parameter. Three main functions are included: QICD cv.QICD BIC.QICD for coefficients estimation and tuning parameter selection respectively. Three other tiny functions are included as a supplement: allzero checkloss QBIC

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 Fan, J. and Li, R.(2001) Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties. Journal of American Statistical Association, 1348-1360. http://orfe.princeton.edu/~jqfan/papers/01/penlike.pdf Zhang,C. (2010) Nearly Unbiase Variable Selection Under Minimax Concave Penalty. The Annals of Statistics, Vol. 38, No.2, 894-942 http://arxiv.org/pdf/1002.4734.pdf

Examples

x=matrix(rnorm(10000),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)