# eigenboot

### Description

A parametric bootstrap procedure evaluated at an envelope estimator
of the submodel mean-value parameter vector *τ* that was
obtained using reducing subspaces.

### Usage

1 2 |

### Arguments

`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 inverse Fisher information is desired to construct envelope estimators |

`data` |
An asterdata object |

`quiet` |
A logical argument. If FALSE, the function
displays how much time it takes to run |

`m` |
The length of the output interval |

### Details

This function implements the parametric bootstrap procedure given by
the algorithm below with respect to the mean-value parameterization.
This parametric bootstrap generates resamples from the distribution
evaluated at an envelope estimator of *τ*. The user specifies which
vectors are used in order to construct envelope estimators using the
reducing subspace approach. When one is using a partial envelope then this
function constructs envelope estimators of *υ* where we write
*τ* = *(γ^T,υ^T)^T* and *υ*
corresponds to aster model parameters of interest. In applications,
candidate reducing subspaces are indices of eigenvectors of *\widehat{Σ}_{υ,υ}*
where *\widehat{Σ}_{υ,υ}* is the part of *\widehat{Σ}*
corresponding to our parameters of interest. When all of the
components of *τ* are components of interest, then we write
*\widehat{Σ}_{υ,υ} = \widehat{Σ}*. The algorithm is as follows:

[1.] Fit the aster model to the data and obtain

*\hat{τ} = (\hat{γ}^T, \hat{υ}^T)*and*\widehat{Σ}*from the aster model fit.[2.] Compute the envelope estimator of

*υ*in the original sample, given as*\hat{υ}_{env} = P_{\hat{G}}\hat{υ}*where*P_{\hat{G}}*is the projection into the reducing subspace of*\widehat{Σ}_{υ,υ}*specified by`vectors`

.[3.] Perform a parametric bootstrap by generating resamples from the distribution evaluated at

*\hat{υ}_{env}*. For iteration*b=1,...,B*of the procedure:[(3a)] Compute

*\hat{υ}^{(b)}*and*\widehat{Σ}_{υ,υ}^{(b)}*from the aster model fit to the resampled data.[(3b)] Obtain

*P_{\hat{G}}^{(b)}*as done in Step 2.[(3c)] Store

*\hat{υ}_{env}^{(b)} = P_{\hat{G}}^{(b)}\hat{υ}^{(b)}*.

A parametric bootstrap generating resamples from the distribution evaluated at the aster model MLE is also conducted by this function.

### Value

`u` |
The dimension of the envelope space assumed |

`table` |
A table of output. The first two columns display the envelope estimator and its bootstrapped standard error. The next two columns display the MLE and its bootstrapped standard error. The last column displays the ratio of the standard error for the bootstrapped envelope estimator to the standard error for the bootstrapped MLE. |

`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. |

### References

Eck, D. J., Geyer, C. J., and Cook, R. D. (2016).
Enveloping the aster model.
*\emph{in prep}*.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
## 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)
``` |