ECD {TRES}

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.

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.

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.

References

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

Examples

##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)