The Efficiency of the Bootstrap Snder a Locally Random Assumption for Systematic Samples

• Activity Number: 363
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Steven F. Kaufman*+
• Companies: U.S. Department of Education
• Keywords: BHR ; SASS ; simulation

Abstract

Many complex sample designs select PSUs systematically with probabilities proportional to some measure of size (PPS). This is generally done to improve efficiency of sample estimates. Since no unbiased variance estimator exists for this type of sample design, assumptions must be made to produce a sample variance estimator. When sampling rates are large, these assumptions should also incorporate an appropriate finite population correction (FPC). One common assumption is that the correlation between pairs of selected PSUs is zero. If one additionally assumes that PSUs are in a locally random order before sample selection, then the appropriate FPC can be derived. The variance estimator implied by these assumptions can easily be implemented using balanced half-sample replication or a bootstrap method. Both a balanced and nonbalanced bootstrap methodology will be studied. Through a simulation study, this paper investigates which methodology produces the best variance estimator in terms of mean square error and the coverage rate. NCES's School and Staffing Survey sample design will be used in the simulation study.