envlpaster (version 0.1-2)

manifold1Dplus: manifold1Dplus

Description

The 1D algorithm

Usage

manifold1Dplus(M,U,u)

Arguments

M

A $\sqrt{n}$ estimate of an estimator's asymptotic covariance matrix.

U

A $\sqrt{n}$ estimate of the parameter associated with the space we are enveloping. For our purposes this quantity is either the outer product of the MLE of the mean-value submodel parameter vector with itself or the outer product of the

u

The dimension of the envelope space assumed.

Value

• G
  A $\sqrt{n}$ estimator of the basis matrix for the envelope subspace. This matrix has u columns

Details

This function calls get1Dobj, get1Dini, and get1Dderiv in order to find $$\max_{w} \left[ \log(w^TMw) + \log(w^T(M+U)w) - 2\log(w^Tw) \right]$$

using Polak-Ribiere conjugate gradient in optim. This maximization is conducted a total of u times and at each iteration a vector belonging to the envelope space is returned. The vector returned at a specific iteration is orthogonal to the vectors returned at previous iterations. When finished, a basis matrix for the envelope space is returned.

References

Cook, R.D. and Zhang, X. (2014). Foundations for Envelope Models and Methods. JASA, In Press.

Cook, R.D. and Zhang, X. (2015). Algorithms for Envelope Estimation. Journal of Computational and Graphical Statistics, Published online. 10.1080/10618600.2015.1029577.

Examples

library(envlpaster)
data(simdata30nodes)
data <- simdata30nodes.asterdata
nnode <- length(vars)
xnew <- as.matrix(simdata30nodes[,c(1:nnode)])
m1 <- aster(xnew, root, pred, fam, modmat)
avar <- m1$fisher
beta <- m1$coef
U <- beta %o% beta
manifold1Dplus(M = avar, U = U, u = 1)