FUNCTIONAL CENTRAL LIMIT THEOREMS FOR SINGLE-STAGE SAMPLING DESIGNS

• 成果类型: Article
• 署名作者: Boistard, Helene; Lopuhaa, Hendrik P.; Ruiz-Gazen, Anne
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Delft University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1507
• 发表日期: 2017
• 页码: 1728-1758
• 关键词: jackknife variance estimator; weighted likelihood; stratified samples; inference; linearization; CONVERGENCE; INEQUALITY; poverty; models

摘要

For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz-Thompson empirical process and the Hajek empirical process centered by their finite population mean as well as by their super-population mean in a survey sampling framework. The results apply to single-stage unequal probability sampling designs and essentially only require conditions on higher order correlations. We apply our main results to a Hadamard differentiable statistical functional and illustrate its limit behavior by means of a computer simulation.