On asymptotic normality and variance estimation for nondifferentiable survey estimators
成果类型：
Article
署名作者：
Wang, Jianqiang C.; Opsomer, J. D.
署名单位：
Colorado State University System; Colorado State University Fort Collins
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asq077
发表日期：
2011
页码：
91106
关键词：
摘要：
Survey estimators of population quantities such as distribution functions and quantiles contain nondifferentiable functions of estimated quantities. The theoretical properties of such estimators are substantially more complicated to derive than those of differentiable estimators. In this article, we provide a unified framework for obtaining the asymptotic design-based properties of two common types of nondifferentiable estimators. Estimators of the first type have an explicit expression, while those of the second are defined only as the solution to estimating equations. We propose both analytical and replication-based design-consistent variance estimators for both cases, based on kernel regression. The practical behaviour of the variance estimators is demonstrated in a simulation experiment.