Estimators Based on Several Stratified Samples with Applications to Multiple Frame Surveys
基于多个分层样本的估计量及其多抽样框调查应用AI 解读 ↓
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基于多个分层样本的估计量及其多抽样框调查应用
- 研究问题
- 在多个抽样框分别独立抽取分层简单随机样本、且能识别重复入样单位时，如何合并样本构造总体估计量？
- 方法与思路
- 作者将多抽样框样本视为同一抽样框上独立抽取多个样本的特例，应用 Horvitz–Thompson、比率及 raking 比率估计。
- 材料陈述的贡献
- 摘要称调查例子中部分估计量比 Hartley 估计量方差更低，计算和多框扩展更简便，并建议数值线性化处理方差。
- 阅读关注点
- 应核对重叠单位识别、合并样本的入样概率、各估计量的比较条件，以及反复数值线性化的操作和方差依据。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化；较低方差只针对某些例子，更复杂设计的具体结果未说明。
原文摘要
In this article, a new method for producing estimates from a multiple frame survey is presented. The discussion in this article is restricted to sample designs in which a stratified simple random sample is selected independently from each frame. The estimation technique outlined, however, can be applied to more complex sample designs. It is assumed that units selected in more than one sample can be identified. This estimation technique is based on the fact that a multiple frame sample can be viewed as a special case of selecting two or more samples independently from the same frame. As a result, standard techniques from the literature for estimating from a single frame, such as the Horvitz—Thompson estimator or ratio estimation, can be applied to multiple frame samples. These standard techniques for estimating from a single frame are compared, based on data from a Statistics Canada survey, with the usual estimators suggested in the literature for estimating from a multiple frame sample design. These multiple frame estimators were first proposed by Hartley (1962). They have a common feature of averaging together separate estimates from two or more frames of the domains corresponding to the overlap of these frames. The numerical example given shows that the estimators suggested in this article provide lower variances in certain cases than the Hartley estimators. These estimators are also simpler to compute and extend more easily to three or more frames than the Hartley estimators. One of the single frame estimators considered is the raking ratio estimator. The complexity of its variance formula has discouraged its use in the past. In the numerical example, it is suggested that this problem can be circumvented by the simple technique of numerically linearizing the values of the observations repeatedly.