LassoSIR-Package {LassoSIR}

Sparsed Sliced Inverse Regression via Lasso

Description

Estimate the sufficient dimension reduction space using sparsed sliced inverse regression via Lasso (Lasso-SIR) introduced in Lin, Zhao, and Liu (2017) <arxiv:1611.06655>. The Lasso-SIR is consistent and achieve the optimal convergence rate under certain sparsity conditions for the multiple index models.

Details

The DESCRIPTION file:

Package:	LassoSIR
Type:	Package
Title:	Sparsed Sliced Inverse Regression via Lasso
Version:	0.1.1
Date:	2017-12-06
Author:	Zhigen Zhao, Qian Lin, Jun Liu
Maintainer:	Zhigen Zhao <[e-mail]>
Description:	Estimate the sufficient dimension reduction space using sparsed sliced inverse regression via Lasso (Lasso-SIR) introduced in Lin, Zhao, and Liu (2017) <arxiv:1611.06655>. The Lasso-SIR is consistent and achieve the optimal convergence rate under certain sparsity conditions for the multiple index models.
License:	GPL-3
Imports:	glmnet, graphics, stats

Index of help topics:

LassoSIR                LassoSIR
LassoSIR-Package        Sparsed Sliced Inverse Regression via Lasso

LassoSIR

Author(s)

Zhigen Zhao, Qian Lin, Jun Liu

Maintainer: Zhigen Zhao <[e-mail]>

References

Qian Lin, Zhigen Zhao, Jun S. Liu (2017) On consistency and sparsity for sliced inverse regression in high dimensions. Annals of Statistics. https://arxiv.org/abs/1507.03895

Qian Lin, Zhigen Zhao, Jun S. Liu (2017) Sparse Sliced Inverse Regression for High Dimensional Data. https://arxiv.org/abs/1611.06655

See Also

NA

Examples

p <- 10
n <- 200


H <- 20
m <- n/H

beta <- array(0, c(p, 1) )
beta[1:3,1] <- rnorm(3, 0, 1)

X <- array(0, c(n, p ) )

rho <- 0.3
Sigma <- diag(p)
elements <- rho^(c((p-1):0,1:(p-1) ) )
for(i in 1:p)
    Sigma[i,] <- elements[(p+1-i):(2*p-i) ]


X <- matrix( rnorm(p*n), c(n, p) )
X <- X%*% chol(Sigma)

Y <-  ( X%*% beta )^3/2 + rnorm(n,0,1)
sir.lasso <- LassoSIR( X, Y, H, choosing.d="automatic",
          solution.path=FALSE, categorical=FALSE, nfolds=10,
          screening=FALSE)
beta.hat <- sir.lasso$beta/sqrt( sum( sir.lasso$beta^2 ) )