TRES (version 1.1.1)

ECD: ECD algorithm for estimating the envelope subspace

Description

Estimate the envelope subspace with specified dimension based on ECD algorithm proposed by Cook, R. D., & Zhang, X. (2018).

Usage

ECD(M, U, u, maxiter=500, tol=1e-08)

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.

u

Envelope dimension. An integer between 0 and \(p\).

maxiter

Maximum number of iterations.

tol

Convergence criterion. \(|F_k - F_{k-1}|<\)tol, where \(F_k\) is the objective function.

Value

Return the orthogonal basis of the envelope subspace with each column represent the sequential direction. For example, the 1st column is the most informative direction.

Details

Estimate M-envelope of span(U) where M > 0. The dimension of the envelope is u.

References

Cook, R. D., & Zhang, X. (2018). Fast envelope algorithms. Statistica Sinica, 28(3), 1179-1197.

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

Gamma_ECD <- ECD(Mhat, Uhat, u=5)
# }