TRES (version 1.1.5)

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, ...)

Arguments

M

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

U

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

u

An integer between 0 and \(n\) representing the envelope dimension.

...

Additional user-defined arguments:

• maxiter: The maximal number of iterations.

• tol: The tolerance used to assess convergence. See the ECD algorithm in Cook, R. D., & Zhang, X. (2018).

The default values are: maxiter=500; tol=1e-08.

Value

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

Details

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

See FGfun for the generic objective function.

The ECD algorithm is similar to 1D algorithm proposed by Cook, R. D., & Zhang, X. (2016). A fast and stable algorithm is used for solving each individual objective function.

References

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

Examples

# NOT RUN {
##simulate two matrices M and U with an envelope structure#
data <- MenvU_sim(p = 20, u = 5, wishart = TRUE, n = 200)
M <- data$M
U <- data$U
G <- data$Gamma
Gamma_ECD <- ECD(M, U, u=5)
subspace(Gamma_ECD, G)

# }