RBS

R package "rbs" providing a procedure to select the response variables and estimate regression coefficients simultaneously. It also provides the screening procedure based on the distance correlation (Szekely and Rizzo (2009) and Li, Zhong and Zhu (2012)), the solution to the quadratic 0-1 programming problems by transferring to k-flipping optimization problems and to continuous quadratic programming problems, and the multiple test procedure including Benjamini-Hochberg and Bonferroni correction. The screening procedure based on the martingale difference correlation (MDC) is provided in other R package (https://github.com/xliusufe/hdtest).

Installation

#install.packages("devtools")
library(devtools)
install_github("xliusufe/rbs")

Usage

• rbs-manual.pdf ---------- Details of the usage of the package.
• rbs ------------------------ The corresponding Python package

Example

library(rbs)

n   <- 200
p   <- 5
q   <- 10
q0  <- 5

Sigma <- matrix(0,q,q)
for(i in 1:q) for(j in 1:q) Sigma[i,j]=0.5^(abs(i-j))
A <- chol(Sigma)
V <- solve(Sigma)

beta <- matrix(runif(p*q0),p,q0)
eps <- matrix(rnorm(n*q),n,q)

x <- matrix(rnorm(n*p),n,p)
y <- cbind(x%*%beta, matrix(0,n,q-q0)) + eps%*%A

fit <- rbs(x,y,criteria=0)
fit$delta

fit <- rbs(x,y)
fit$delta
fit$selected

fit <- rbs_sig(x,y,criteria=0)
fit$delta


fit <- rbs_sig(x,y,V,criteria=0)
fit$delta


lambda <- seq(0.01, 2, length = 50)
fit <- rbs_sig(x,y,lambda=lambda)
fit$delta
fit$selected

fit <- rbs_sig(x,y,V,lambda=lambda)
fit$delta
fit$selected

fit <- pval(x,y)
fit$Tn
fit$pvals
fit$pvfdr
fit$signifc

References

Benjamini, Y. and Hochberg, Y. (1995). Controlling the False Discovery Rate A Practical and Powerful Approach to Multiple testing. Journal of the Royal Statistical Society: Series B (Methodological). 57(1), 289-300.

Chen, W. and L. Zhang (2010). Global Optimality Conditions for Quadratic 0-1 Optimization Problems. Journal of Global Optimization 46(2), 191-206.

Chen, W. (2015). Optimality Conditions for the Minimization of Quadratic 0-1 Problems. SIAM Journal on Optimization, 25(3), 1717-1731.

Hu, J., Huang, J., Liu, X. and Liu, X. (2020). Response Best-subset Selector for Multivariate Regression. Manuscript.

Li, R., W. Zhong, and L. Zhu (2012). Feature Screening Via Distance Correlation Learning. Journal of the American Statistical Association, 107 (499), 1129-1139.

Szekely, G.J. and Rizzo, M.L. (2009). Brownian Distance Covariance, Annals of Applied Statistics, 3(4), 1236-1265.

Szekely, G.J. and Rizzo, M.L. (2009). Rejoinder: Brownian Distance Covariance, Annals of Applied Statistics, 3(4), 1303-1308.

Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007). Measuring and Testing Dependence by Correlation of Distances, Annals of Statistics, 35(6), 2769-2794.

Development

This R package is developed by Xu Liu (liu.xu@sufe.edu.cn).