Description Usage Arguments Details Value References Examples

A parametric bootstrap procedure evaluated at an envelope estimator
of the submodel mean-value parameter vector *τ* that was
obtained using the 1D algorithm.

1 2 | ```
targetboot(model, nboot, index, u, data,
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 |

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

`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 |

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*. Envelope estimators are
constructed using the 1D algorithm at a user-specified envelope model
dimension `u`

. 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 the sample, the
1D algorithm uses *M = \widehat{Σ}_{υ,υ}* and
*U = \hat{τ}\hat{τ}^T* as inputs 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{\mathcal{E}}}\hat{υ}*where*P_{\hat{\mathcal{E}}}*is obtained from the 1D algorithm.[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{\mathcal{E}}}^{(b)}*as done in Step 2.[(3c)] Store

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

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 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. |

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*.

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 <- targetboot(m1, nboot = nboot, index = target,
u = u, data = data, m = timer)
bar
## End(Not run)
``` |

envlpaster documentation built on May 29, 2017, 3:31 p.m.

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