Sample Expansion for Probability Proportional to Size Without Replacement Sampling

摘要

There exist numerous methods for selecting a fixed size sample with probability proportional to size (PPS), without replacement. Brewer and Hanif (1983) describe 50 such procedures and detail the properties of each of these procedures. The properties described are with respect to the selection of a single sample directly from the universe. However, sometimes it may be necessary to either select a subsample of the original sample or to expand the original sample to a larger sample from the same universe, where in either case the new sample is also to be a fixed size sample selected PPS, without replacement from the original universe with the original measures of size. In the case of subsampling, if the procedure used to select the original sample is strictly PPS, without replacement, then subsampling with the desired properties can always be done.