BIC_PFP {SILFS}

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
)

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.

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.

Author(s)

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)

BIC_PFP(Y,F_1,U,alpha_init,lasso_start,lasso_stop,lam_start,lam_stop,grid_1,grid_2,0.3)