# rescaled.bootstrap.sample

### Description

C++ version: given a survey dataset and a description of the survey design (ie, which combination of vars determines primary sampling units, and which combination of vars determines strata), take a bunch of bootstrap samples for the rescaled bootstrap estimator (see, eg, Rust and Rao 1996).

### Usage

1 2 | ```
rescaled.bootstrap.sample(survey.data, survey.design, parallel = FALSE,
paropts = NULL, num.reps = 1)
``` |

### Arguments

`survey.data` |
the dataset to use |

`survey.design` |
a formula describing the design of the survey (see below - TODO) |

`parallel` |
if TRUE, use parallelization (via |

`paropts` |
an optional list of arguments passed on to |

`num.reps` |
the number of bootstrap replication samples to draw |

### Details

Note that we assume that the formula uniquely specifies PSUs. This will always be true if the PSUs were selected without replacement. If they were selected with replacement, then it will be necessary to make each realization of a given PSU in the sample a unique id. Bottom line: the code below assumes that all observations within each PSU (as identified by the design formula) are from the same draw of the PSU.

The rescaled bootstrap technique works by adjusting the estimation weights based on the number of times each row is included in the resamples. If a row is never selected, it is still included in the returned results, but its weight will be set to 0. It is therefore important to use estimators that make use of the estimation weights on the resampled datasets.

We always take m_i = n_i - 1, according to the advice presented in Rao and Wu (1988) and Rust and Rao (1996).

`survey.design`

is a formula of the form

weight ~ psu_vars + strata(strata_vars),
where weight is the variable with the survey weights and psu
is the variable denoting the primary sampling unit

### Value

a list with `num.reps`

entries. each entry is a dataset which
has at least the variables `index`

(the row index of the original
dataset that was resampled) and `weight.scale`

(the factor by which to multiply the sampling weights
in the original dataset).