manifold1Dplus {envlpaster} | R Documentation |
The 1D algorithm
manifold1Dplus(M,U,u)
M |
A √{n} estimate of an estimator's asymptotic covariance matrix. |
U |
A √{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 MLE of the canonical submodel parameter vector with itself. |
u |
The dimension of the envelope space assumed. |
This function calls get1Dobj
, get1Dini
, and get1Dderiv
in order to find
\max_{w} ≤ft[ \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.
G |
A √{n} estimator of the basis matrix for the
envelope subspace. This matrix has |
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. doi: 10.1080/10618600.2015.1029577.
## Not run: 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) ## End(Not run)