BIC_SILFS {SILFS}

Selecting Tuning Parameter for SILFS Method via corresponding BIC

Description

This function is to select tuning parameters simultaneously for SILFS method via minimizing the BIC.

Usage

BIC_SILFS(
  Y,
  Fhat,
  Uhat,
  K,
  alpha_init,
  lasso_start,
  lasso_stop,
  CAR_start,
  CAR_stop,
  grid_1,
  grid_2,
  epsilon
)

Arguments

Y

The response vector of length n.

Fhat

The estimated common factors matrix of size n \times r.

Uhat

The estimated idiosyncratic factors matrix of size n \times p.

K

The estimated subgroup number.

alpha_init

The initialization of intercept parameter.

lasso_start

The user-supplied start search value of the tuning parameters for LASSO.

lasso_stop

The user-supplied stop search value of the tuning parameters for LASSO.

CAR_start

The user-supplied start search value of the tuning parameters for Center-Augmented Regularization.

CAR_stop

The user-supplied stop search value of the tuning parameters for Center-Augmented Regularization.

grid_1

The user-supplied number of search grid points corresponding to the LASSO tuning parameter.

grid_2

The user-supplied number of search grid points corresponding to the tuning parameter for Center-Augmented Regularization.

epsilon

The user-supplied stopping tolerance.

Value

A list with the following components:

lasso

The tuning parameter of the LASSO penalty selected using BIC.

CAR

The tuning parameter of the Center Augmented Regularization selected using BIC.

Examples

n <- 50
p <- 50
r <- 3
K <- 2
lasso_start <- sqrt(log(p)/n)*0.01
lasso_stop <- sqrt(log(p)/n)*10^(0.5)
CAR_start <- 0.001
CAR_stop <- 0.1
grid_1 <- 5
grid_2 <- 5
alpha <- sample(c(-3,3),n,replace=TRUE,prob=c(1/2,1/2))
beta <- c(rep(1,2),rep(0,48))
B <- matrix((rnorm(p*r,1,1)),p,r)
F_1 <- matrix((rnorm(n*r,0,1)),n,r)
U <- matrix(rnorm(p*n,0,0.1),n,p)
X <- F_1%*%t(B)+U
Y <- alpha + X%*%beta + rnorm(n,0,0.5)
alpha_init <- INIT(Y,F_1,0.1)

BIC_SILFS(Y,F_1,U,K,alpha_init,lasso_start,lasso_stop,CAR_start,CAR_stop,grid_1,grid_2,0.3)