TRES (version 0.1.0)

ballGBB1D_bic: Envelope dimension selection based on 1D-BIC

Description

This function selects envelope subspace dimension use 1D-BIC 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, bic_max=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, see Zhang, X., & Mai, Q. (2018), the default value is 1.

bic_max

The maximum dimension to consider, bic_max 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

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

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