SILFS (version 0.1.0)

BIC_PFP: Selecting Tuning Parameter for Factor Adjusted-Pairwise Fusion Penalty (FA-PFP) Method via corresponding BIC

Description

This function is to select tuning parameters simultaneously for FA-PFP method via minimizing the BIC.

Usage

BIC_PFP(
  Y,
  Fhat,
  Uhat,
  alpha_init,
  lasso_start,
  lasso_stop,
  lam_start,
  lam_stop,
  grid_1,
  grid_2,
  epsilon
)

Value

A list with the following components:

lasso

The tuning parameter of the LASSO penalty selected using BIC.

lambda

The tuning parameter of the Pairwise Concave Fusion Penalty selected using BIC.

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 \(n \times p\).

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.

lam_start

The user-supplied start search value of the tuning parameters for Pairwise Fusion Penalty.

lam_stop

The user-supplied stop search value of the tuning parameters for Pairwise Fusion Penalty.

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 Pairwise Fusion Penalty.

epsilon

The user-supplied stopping tolerance.

Author

Yong He, Liu Dong, Fuxin Wang, Mingjuan Zhang, Wenxin Zhou.

Examples

n <- 50
p <- 50
r <- 3
lasso_start <- sqrt(log(p)/n)*0.1
lasso_stop <- sqrt(log(p)/n)
lam_start <- 0.3
lam_stop <- 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)
# \donttest{
BIC_PFP(Y,F_1,U,alpha_init,lasso_start,lasso_stop,lam_start,lam_stop,grid_1,grid_2,0.3)
# }