Sampling with Unequal Probabilities
Yves G Berger, Yves Tillé
Since the mid-1950s, there has been a well-developed theory of sample survey design inference embracing complex designs with stratification and unequal probabilities. Unequal probability sampling was first suggested by Hansen and Hurwitz in the context of sampling with replacement. Narain, Horvitz, and Thompson developed the corresponding theory for sampling without replacement. A large part of survey-sampling literature is devoted to unequal probability sampling, and more than 50 sampling algorithms have been proposed. Multistage sampling is one of the applications of unequal probability sampling design where the selection of primary units within strata may be done with unequal probability. For example, self-weighted two-stage sampling is often used to select primary sampling units with probabilities that are proportional to the number of secondary sampling units within the primary units; a simple random sample is selected within each primary unit. © 2009 Elsevier Inc.