TRES (version 1.1.1)

ballGBB1D_bic: Envelope dimension selection based on 1D-BIC

Description

This function selects envelope subspace dimension using 1D-BIC proposed by Zhang, X., & Mai, Q. (2018). The constrained optimization in the 1D algorithm is based on the method proposed by Wen and Yin (2013).

Usage

ballGBB1D_bic(M, U, n, multiD=1, maxdim=10, opts=NULL)

Arguments

M

M matrix in the envelope objective function. A \(p\)-by-\(p\) positive semi-definite matrix.

U

U matrix in the envelope objective function. A \(p\)-by-\(p\) positive semi-definite matrix.

n

Sample size.

multiD

A constant, the default value is 1.

maxdim

The maximum dimension to consider, maxdim is smaller than \(p\), the default value is 10.

opts

Option structure for GBB algorithm. See function OptStiefelGBB.

Value

bicval

The BIC values for different envelope dimensions.

u

The dimension selected which corresponds to the smallest BIC values.

References

Zhang, X., & Mai, Q. (2018). Model-free envelope dimension selection. Electronic Journal of Statistics, 12(2), 2193-2216. Wen, Z., & Yin, W. (2013). A feasible method for optimization with orthogonality constraints. Mathematical Programming, 142(1-2), 397-434.

Examples

# NOT RUN {
##simulate two matrices M and U with an envelope structure#
data <- MenvU_sim(n=200, p=20, u=5)
Mhat <- data$Mhat
Uhat <- data$Uhat

fit <- ballGBB1D_bic(Mhat, Uhat, n=200)

## visualization
plot(1:10, fit$bicval, type="o", xlab="Envelope Dimension", ylab="BIC values",
main="Envelope Dimension Selection")
# }