Nonparametric Variance Estimation Under Fine Stratification: An Alternative to Collapsed Strata

• 成果类型: Article
• 署名作者: Breidt, F. Jay; Opsomer, Jean D.; Sanchez-Borrego, Ismael
• 署名单位: Colorado State University System; Colorado State University Fort Collins
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1058264
• 发表日期: 2016
• 页码: 822-833
• 关键词: unequal probabilities; complex surveys; regression; MODEL

摘要

Fine stratification is commonly used to control the distribution of a sample from a finite population and to improve the precision of resulting estimators. One-per-stratum designs represent the finest possible stratification and occur in practice, but designs with very low numbers of elements per stratum (say, two orthree). are also common. The classical variance estimator in this context is the collapsed stratum estimator, which relies on creating larger pseudo-strata and computing the sum of the squared differences between estimated stratum totals across the pseudo-strata. We propose here a nonparametric alternative that replaces the pseudo-strata by kernel-weighted stratum neighborhoods and uses deviations from a fitted mean function to estimate the variance. We establish the asymptotic behavior of the kernel-based-estimator and show its superior practical performance relative to the collapsed stratum variance estimator in a simulation study. An application to data from the U.S. Consumer Expenditure Survey illustrates the potential of the method in practice.