fit.boot {envlpaster}  R Documentation 
A parametric bootstrap procedure evaluated at an envelope estimator
of the submodel meanvalue parameter vector \tau
that was
obtained using reducing subspaces.
fit.boot(model, nboot, index, vectors = NULL, u = NULL,
data, amat, newdata, modmat.new = NULL, renewdata = NULL,
fit.name = NULL, method = c("eigen","1d"), quiet = FALSE, m = 100)
model 
An aster model object. 
nboot 
The number of bootstrap iterations desired. 
index 
The indices denoting which components of the canonical parameter vector are parameters of interest. 
vectors 
The indices denoting which reducing subspace of Fisher information is desired to construct envelope estimators. 
u 
The envelope model dimension. 
data 
An asterdata object corresponding to the original data. 
amat 
This object can either be an array or a matrix.
It specifies a linear combination of meanvalue parameters
that correspond to expected Darwinian fitness. See the

newdata 
A dataframe corresponding to hypothetical individuals in which expected Darwinian fitness is to be estimated. 
modmat.new 
A model matrix corresponding to hypothetical individuals in which expected Darwinian fitness is to be estimated. 
renewdata 
A dataframe in long format corresponding to hypothetical individuals in which expected Darwinian fitness is to be estimated. 
fit.name 
An expression that appears in the name of the
nodes that correspond to Darwinian fitness. This is only
necessary if 
method 
The procedure used to obtain envelope estimators. 
quiet 
A logical argument. If FALSE, the function
displays how much time it takes to run 
m 
The length of the output interval. 
This function implements the parametric bootstrap procedure given by
the algorithm presented below with respect to the meanvalue
parameterization. This parametric bootstrap generates resamples from the distribution
evaluated at an envelope estimator of \tau
.
The user specifies which vectors are used in order to construct envelope
estimators using the reducing subspace approach. The user also specifies which
method is to be used in order to calculate envelope estimators. When one
is using a partial envelope, then this function constructs envelope
estimators of \upsilon
where we write \tau
= (\gamma^T,\upsilon^T)^T
and \upsilon
corresponds to aster model parameters of interest.
In applications, candidate reducing subspaces are indices of eigenvectors of \widehat{\Sigma}_{\upsilon,\upsilon}
where \widehat{\Sigma}_{\upsilon,\upsilon}
is the part of \hat{\Sigma}
corresponding to our parameters of interest. These indices are specified
by vectors
. When all of the components of \tau
are components
of interest, then we write \widehat{\Sigma}_{\upsilon,\upsilon} = \widehat{\Sigma}
. When data
is generated via the parametric bootstrap, it is the indices (not the
original reducing subspaces) that are used to construct envelope estimators
constructed using the generated data. The algorithm using reducing subspaces
is as follows:
[1.] Fit the aster model to the data and obtain
\hat{\tau} = (\hat{\gamma}^T, \hat{\upsilon}^T)
and \hat{\Sigma}
from the aster model fit.
[2.] Compute the envelope estimator of \upsilon
in the original
sample, given as \hat{\upsilon}_{env} = P_{\hat{G}}\hat{\upsilon}
where P_{\hat{G}}
is the projection into the reducing subspace of
\widehat{\Sigma}_{\upsilon,\upsilon}
specified by vectors
.
[3.] Perform a parametric bootstrap by generating resamples from the
distribution evaluated at \hat{\tau}_{env} = (\hat{\gamma}^T,\hat{\upsilon}_{env}^T)^T
.
For iteration b=1,...,B
of the procedure:
[(3a)] Compute \hat{\upsilon}^{(b)}
and
\widehat{\Sigma}_{\upsilon,\upsilon}^{(b)}
from the aster model fit to
the resampled data.
[(3b)] Obtain P_{\hat{G}}^{(b)}
as done in Step 2.
[(3c)] Compute \hat{\upsilon}_{env}^{(b)} = P_{\hat{G}}^{(b)}\hat{\upsilon}^{(b)}
and
\hat{\tau}_{env}^{(b)} = (\hat{\gamma}^{(b)^T},\hat{\upsilon}_{env}^{(b)^T})^T
.
[(3d)] Store h\left(\hat{\tau}_{env}^{(b)}\right)
where h
maps \tau
to the parameterization of Darwinian fitness as determined
by amat
.
The parametric bootstrap procedure which uses the 1d algorithm to construct
envelope estimators is analogous to the above algorithm. To use the 1d
algorithm, the user specifies a candidate envelope model dimension u
and specifies method = "1d"
. A parametric bootstrap generating resamples
from the distribution evaluated at the aster model MLE is also conducted by
this function.
u 
The dimension of the envelope space assumed 
table 
A table of output. The first two columns display the envelope estimator of expected Darwinian fitness and its bootstrapped standard error. The next two columns display the MLE of expected Darwinian fitness and its bootstrapped standard error. The last column displays the ratio of the standard errors using MLE to those using envelope estimation. Ratios greater than 1 indicate efficiency gains obtained using envelope estimation. 
S 
The bootstrap estimator of the variability of the partial envelope estimator. 
S2 
The bootstrap estimator of the variability of the MLE. 
env.boot.out 
The realizations from the bootstrap procedure using envelope methodology. 
MLE.boot.out 
The realizations from the bootstrap procedure using maximum likelihood estimation. 
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.
Eck, D. J., Geyer, C. J., and Cook, R. D. (2016). Enveloping the aster model. in prep.
## Not run: set.seed(13)
library(envlpaster)
library(aster2)
data(simdata30nodes)
data < simdata30nodes.asterdata
nnode < length(vars)
xnew < as.matrix(simdata30nodes[,c(1:nnode)])
m1 < aster(xnew, root, pred, fam, modmat)
target < 5:9
indices < c(1,2,4,5)
u < length(indices)
nboot < 2000; timer < nboot/2
bar < eigenboot(m1, nboot = nboot, index = target,
u = u, vectors = indices, data = data, m = timer)
bar
## End(Not run)