targetbootcanon {envlpaster} | R Documentation |

A parametric bootstrap procedure evaluated at an envelope estimator
of the submodel canonical parameter vector `\beta`

that was
obtained using the 1D algorithm.

```
targetbootcanon(model, nboot, index, u,
code, families, 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. |

`code` |
A vector of dimension equal to the number
of nodes in the aster graph. This vector specifies
which exponential family in the |

`families` |
A list of family specifications. |

`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 canonical
parameterization. This parametric bootstrap generates resamples from the
distribution evaluated at an envelope estimator of `\beta`

. 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 `\upsilon`

where
we write `\tau`

= `(\gamma^T,\upsilon^T)^T`

and `\upsilon`

corresponds to aster model parameters of interest. In the sample, the
1D algorithm uses `M = \widehat{\Sigma}_{\upsilon,\upsilon}^{-1}`

and
`U = \hat{\beta}\hat{\beta}^T`

as inputs where `\widehat{\Sigma}_{\upsilon,\upsilon}^{-1}`

is the part of `\hat{\Sigma}^{-1}`

corresponding to our parameters
of interest. When all of the components of `\tau`

are components of
interest, then we write `\widehat{\Sigma}_{\upsilon,\upsilon}^{-1} = \widehat{\Sigma}^{-1}`

.
The algorithm is as follows:

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

`\hat{\tau} = (\hat{\gamma}^T, \hat{\upsilon}^T)`

and`\widehat{\Sigma}^{-1}`

from the aster model fit.[2.] Compute the envelope estimator of

`\upsilon`

in the original sample, given as`\hat{\upsilon}_{env} = P_{\hat{\mathcal{E}}}\hat{\upsilon}`

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{\upsilon}_{env}`

. For iteration`b=1,...,B`

of the procedure:[(3a)] Compute

`\hat{\upsilon}^{(b)}`

and`\widehat{\Sigma}_{\upsilon,\upsilon}^{(b)^{-1}}`

from the aster model fit to the resampled data.[(3b)] Obtain

`P_{\hat{\mathcal{E}}}^{(b)}`

as done in Step 2.[(3c)] Store

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

```
## Not run: set.seed(13)
library(envlpaster)
library(aster2)
data(generateddata)
m1 <- aster(resp ~ 0 + varb + mass + timing,
fam = fam, pred = pred, varvar = varb, idvar = id,
root = root, data = redata)
target <- c(9:10)
nboot <- 2000; timer <- nboot/2
bar <- targetbootcanon(m1, nboot = nboot, index = target,
u = 1, m = timer)
bar
## End(Not run)
```

[Package *envlpaster* version 0.1-2 Index]