Bootstrap weights for infinite populations ('with replacement' sampling) are created by sampling with
replacement from the PSUs in each stratum. subbootweights()
samples n1
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
singlestage designs with small sampling fractions, where it reduces
to a halfsample replicate method.
1 2 3 4 5 6  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 
fpcs 

compress 
Should the replicate weights be compressed? 
multicore 
Use the 
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()
These bootstraps are strictly appropriate only when the first stage of sampling is a simple or stratified random sample of PSUs with or without replacement, and not (eg) for PPS sampling. The functions will not enforce simple random sampling, so they can be used (approximately) for data that have had nonresponse corrections and other weight adjustments. It is preferable to apply these adjustments after creating the bootstrap replicate weights, but that may not be possible with publicuse data.
Canty AJ, Davison AC. (1999) Resamplingbased variance estimation for labour force surveys. The Statistician 48:379391
Judkins, D. (1990), "Fay's Method for Variance Estimation" Journal of Official Statistics, 6, 223239.
Preston J. (2009) Rescaled bootstrap for stratified multistage sampling. Survey Methodology 35(2) 227234
Rao JNK, Wu CFJ. Bootstrap inference for sample surveys. Proc Section on Survey Research Methodology. 1993 (866–871)
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