Simple design-efficient calibration estimators for rejective and high-entropy sampling

• 成果类型: Article
• 署名作者: Tan, Z.
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass090
• 发表日期: 2013
• 页码: 399415
• 关键词: empirical likelihood; auxiliary information; Robustness; prediction; inference; variance; models

摘要

For survey calibration, consider the situation where the population totals of auxiliary variables are known or where auxiliary variables are measured for all population units. For each situation, we develop design-efficient calibration estimators under rejective or high-entropy sampling. A general approach is to extend efficient estimators for missing-data problems with independent and identically distributed data to the survey setting. We show that this approach effectively resolves two long-standing issues in existing approaches: how to achieve design efficiency regardless of a linear superpopulation model in generalized regression and calibration estimation, and how to find a simple approximation in optimal regression estimation. Moreover, the proposed approach sheds light on several issues that seem not to be well studied in the literature. Examples include use of the weighted Kullback-Leibler distance in calibration estimation, and efficient estimation allowing for misspecification of a nonlinear superpopulation model.