Abstract: Based on a few basic requirements on bootstraps, we derive the proper bootstrap resampling scheme for SRS (simple random sampling without replacement in a finite population). This concept is then extended to unequal probability samplings. We show that these definitions lead to no ambiguous bootstraps whether we treat the stratified populations as a whole population or through structured conditioning. Stratified and two stage samplings are included.
Key words and phrases: Bootstrap, maximum likelihood summary, simple random sampling, stratified random sampling, two stage sampling.