Bootstrap weights for infinite populations ('with replacement' sampling) are created by sampling with
replacement from the PSUs in each stratum. `subbootweights()`

samples `n-1`

PSUs from the `n`

available (Rao and Wu),
`bootweights`

samples `n`

(Canty and Davison).

For multistage designs or those with large sampling fractions,
`mrbweights`

implements Preston's multistage rescaled
bootstrap. The multistage rescaled bootstrap is still useful for
single-stage designs with small sampling fractions, where it reduces
to a half-sample replicate method.

```
bootweights(strata, psu, replicates = 50, fpc = NULL,
fpctype = c("population", "fraction", "correction"),
compress = TRUE)
subbootweights(strata, psu, replicates = 50, compress = TRUE)
mrbweights(clusters, stratas, fpcs, replicates=50,
multicore=getOption("survey.multicore"))
```

strata

Identifier for sampling strata (top level only)

stratas

data frame of strata for all stages of sampling

psu

Identifier for primary sampling units

clusters

data frame of identifiers for sampling units at each stage

replicates

Number of bootstrap replicates

fpc

Finite population correction (top level only)

fpctype

Is `fpc`

the population size, sampling fraction,
or 1-sampling fraction?

fpcs

`survey_fpc`

object with population and sample size at each stage

compress

Should the replicate weights be compressed?

multicore

Use the `multicore`

package to generate the replicates in parallel

A set of replicate weights

With `multicore=TRUE`

the resampling procedure does not
use the current random seed, so the results cannot be exactly
reproduced even by using `set.seed()`

Canty AJ, Davison AC. (1999) Resampling-based variance estimation for labour force surveys. The Statistician 48:379-391

Judkins, D. (1990), "Fay's Method for Variance Estimation" Journal of Official Statistics, 6, 223-239.

Preston J. (2009) Rescaled bootstrap for stratified multistage sampling. Survey Methodology 35(2) 227-234

Rao JNK, Wu CFJ. Bootstrap inference for sample surveys. Proc Section on Survey Research Methodology. 1993 (866--871)