simplsMU {TRES}

SIMPLS-type algorithm for estimating the envelope subspace

Description

This algorithm is a generalization of the SIMPLS algorithm in De Jong, S. (1993). See Cook (2018) Section 6.5 for more details of this generalized moment-based envelope algorithm; see Cook, Helland, and Su (2013) for a connection between SIMPLS and the predictor envelope in linear model.

Usage

simplsMU(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.

Value

Returns the estimated orthogonal basis of the envelope subspace.

References

De Jong, S., 1993. SIMPLS: an alternative approach to partial least squares regression. Chemometrics and intelligent laboratory systems, 18(3), pp.251-263.

Cook, R.D., Helland, I.S. and Su, Z., 2013. Envelopes and partial least squares regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(5), pp.851-877.

Cook, R.D., 2018. An introduction to envelopes: dimension reduction for efficient estimation in multivariate statistics (Vol. 401). John Wiley & Sons.

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_pls <- simplsMU(M, U, u=5)
subspace(Gamma_pls, G)