On the Efficiency of Raking Ratio Estimation for Multiple Frame Surveys
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多抽样框调查中迭代比例估计的效率
- 研究问题
- 组合不同抽样框的样本时，迭代比例估计能否一致估计总体总量，其渐近效率与其他多框估计方法相比如何？
- 方法与思路
- 作者主要分析经典非分层双框情形，推导迭代次数增加时估计量的极限闭式表达、一致性与渐近方差，并进行效率比较。
- 材料陈述的贡献
- 摘要称，在所分析框架内，极限估计量的效率始终低于 Fuller–Burmeister 估计量，但某些特殊情形损失较小且扩展方便。
- 阅读关注点
- 应核对双框重叠信息、抽样设计及渐近条件，区分迭代次数极限与样本量渐近，并检查多框及分层扩展的具体处理。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；主要理论限于经典非分层双框情形，效率结论不能任意外推。
原文摘要
Multiple frame surveys involve the combination of samples selected from separate sampling frames. A topical example is a dual-frame survey that combines a sample of households interviewed by telephone with a sample drawn from a frame including nontelephone households. Various estimators of population totals and means have been proposed for multiple frame surveys. In particular Bankier proposed the application of raking ratio estimation and compared its performance to alternative estimators in a numerical study based on dual-frame Statistics Canada data. He concluded that the raking ratio estimator performed well but gave no theoretical results to support his empirical findings. This article provides a theoretical study of the efficiency of the raking ratio estimator for multiple-frame surveys. Attention is restricted mainly to the classical, unstratified two-frame case considered by Hartley. For the estimation of totals, we give a closed-form expression for the limiting form of the raking ratio estimator as the number of iterations increases. We show that this limiting estimator is consistent and obtain an expression for its asymptotic variance. Using this expression we show that this estimator is uniformly less efficient than an estimator proposed by Fuller and Burmeister. However, the loss of efficiency is small in some special cases. The raking ratio estimator has the advantage that it extends simply to more than two frames and to stratified sampling, whereas the corresponding extension of the Fuller–Burmeister estimator is more problematic.