A NOTE ON THE LARGE SAMPLE PROPERTIES OF LINEARIZATION, JACKKNIFE AND BALANCED REPEATED REPLICATION METHODS FOR STRATIFIED SAMPLES

• 成果类型: Note
• 署名作者: KORN, EL; GRAUBARD, BI
• 署名单位: National Institutes of Health (NIH) - USA; NIH National Cancer Institute (NCI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348400
• 发表日期: 1991
• 页码: 2275-2279
• 关键词: STATISTICS; inference

摘要

Krewski and Rao consider inference for a (nonlinear) function of a vector of finite population means 0 = g(YBAR). For a sequence of finite populations with increasing number of strata, they demonstrate that theta = g(yBAR) is asymptotically normal, where yBAR is the usual unbiased stratified estimator of YBAR. Additionally, they demonstrate that (theta - theta)/upsilon1/2(theta) is asymptotically a standard normal distribution, where upsilon(theta) is a variance estimator obtained using linearization, jackknife or balanced repeated replication (BRR) methods. In this note we extend their results to when the partial first derivatives (g1(mu), g2(mu),..., g(p)(mu)) = 0, where mu is the limit of YBAR with increasing number of strata. We explore the asymptotic distribution of (theta - theta)/upsilon1/2(theta) and show (1) that it is no longer normal and (2) that it depends upon which variance estimator is used. We describe an application of these results to hypothesis testing using complex survey data.