Developments in Sampling with Unequal Probabilities: Brewer's Contributions

• Activity Number: 46 - In Memory of Ken Brewer
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: Memorial
• Author(s): J.N.K. Rao and David Haziza*
• Companies: Carleton University and University of Ottawa
• Keywords: incluson probabilities; multistage sampling; primary sampling units

Abstract

Stratified multistage sampling is often used in large-scale sample surveys, and primary sampling units (PSUs) within strata are selected with inclusion probabilities proportional to size (IPPS). Development of relevant theory for such designs is theoretically challenging. In 1963, Ken Brewer developed an ingenious IPPS method for the selection of two PSUs per stratum that permitted the evaluation of joint inclusion probabilities explicitly and in turn unbiased variance estimators. In 1982, he wrote a superb monograph on sampling with unequal probabilities. In 2003, he studied the case of more than two PSUs per stratum and developed useful approximations to the joint inclusion probabilities in terms of marginal inclusion probabilities. We provide an appraisal of Brewer’s seminal work on unequal probability sampling without replacement.