Estimators Based on Several Stratified Samples with Applications to Multiple Frame Surveys
提出一种将多框架样本视为从同一框架独立抽取多个样本的新估计方法，可应用单框架标准技术（如Horvitz-Thompson估计量），在加拿大统计局数据中比Hartley估计量方差更低且计算更简单。
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.