Double Sampling in a Multistage Design

• Activity Number: 389
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): David R. Judkins*+ and Mike Hidiroglou
• Companies: Westat and Office of National Statistics
• Keywords: variance estimation ; PPS selection ; survey design

Abstract

It often happens in a multistage design that useful auxiliary information is available on the final stage units. A common practice is to use this information in some sort of systematic PPS selection within the penultimate stage units, either drawing a new random start for each penultimate-stage unit or carrying the leftover to determine the starting point in the next unit. It is known that carry-over introduces some biases in the variance estimates, but many place more importance on variance minimization than on unbiased or consistent variance estimation. This emphasis may be most common when the final-stage strata correspond to analytic domains and there are required precision levels for each domain. In such cases, it is not uncommon to use systematic PPS selection where the primary sort key is the final stage stratum and the earlier stages of sampling are completely ignored. In this case, both the impact on true variances and on the bias of estimated variances can be quite large. We propose a sampling method that satisfies constraints on sample sizes by final-stage stratum, keeps variances small, and admits unbiased variance estimates for linear statistics and consistent variance estimates for nonlinear statistics. The variance estimator proposed for use with this sampling method is new.