QICD-package: Estimation of coefficients of nonconvex penalized quantile...

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

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

Author(s)

Bo Peng

Maintainer: Bo Peng, [e-mail]

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

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)

Example output

QICD documentation built on May 29, 2017, 3:04 p.m.