Generalized Variance Functions in Stratified Two-Stage Sampling
分层两阶段抽样中的广义方差函数AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究调查抽样的方差发布与估计，未提供因果、面板或其他所列细分领域的直接证据。
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分层两阶段抽样中的广义方差函数
- 研究问题
- 在分层两阶段整群抽样中，能否用总量的函数简便估计相对抽样方差，并在何种预测模型下保证一致性？
- 方法与思路
- 作者采用有限总体抽样的预测观点，研究簇均值线性组合的渐近性质，以 a+b/T 型函数建模并用家庭数据模拟检验。
- 材料陈述的贡献
- 摘要称，特定预测模型下一种估计量一致；所述模拟中加权最小二乘拟合表现最佳，但稀有特征和部分变量存在局限。
- 阅读关注点
- 核对层内均值方差、簇内相关与簇间不相关条件，变量选择和加权规则，以及偏差、精度与区间覆盖的比较标准。
- 阅读边界
- 仅依据版本未注明的 OpenAlex 索引摘要；模拟结论限于所述家庭数据与抽样设计，摘要也明确指出不存在适合所有调查变量的方差函数。
原文摘要
Generalized variance functions (GVF's) are used in a number of sample surveys as a convenient method of publishing sampling errors. The method consists of estimating the relative variance (relvariance) of an estimator of a total T by using a model with the form a + b/T. Using the prediction approach to finite population sampling, some asymptotic theory is presented for estimators of totals that are linear combinations of sample cluster means from stratified, two-stage cluster samples. One choice of GVF estimator is shown to be consistent under a particular class of prediction models. The theory is illustrated by an empirical study in which two-stage stratified samples are selected from a population of households. The prediction model is one in which units within a stratum have a common mean and variance, units in the same cluster are correlated but units in different clusters are not, and in which the common variance is a quadratic function of the common mean in a stratum. Bernoulli and Poisson random variables, for example, have the mean-to-variance relationship studied here. Under the model the approximate prediction-relvariance of has the form a + b/T, and the parameters a and b can be estimated by least squares. The theory leads to guidelines for selecting a set of survey variables to use in estimating a and b. The theory was tested in a simulation study using household data collected in the U.S. Current Population Survey. Totals of binary variables derived from labor force and demographic data were estimated in 2,000 stratified two-stage samples. Using 45 variables, I estimated GVF's of the form a + b/T and cTd , which has been suggested elsewhere in the literature, from each sample and summarized results over all samples. The results illustrate that some GVF's can, for many variables, produce unbiased estimators of relvariance that are more precise than a direct, point estimator, and that also have reasonably good confidence interval coverage properties. The best choice of GVF was based on a weighted least squares fit of the model a + b/T. Two limitations of GVF's are that they may not perform particularly well for rare characteristics and that there will inevitably be survey variables for which no GVF will be appropriate.