Jackknife Variance Estimation under Imputation for Estimators Using Poststratification Information
插补下使用后分层信息的估计量的刀切方差估计AI 解读 ↓
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插补下使用后分层信息的估计量的刀切方差估计
- 研究问题
- 调查估计使用后分层信息且存在单位或项目无响应时，如何构造刀切方差估计，并保证其渐近一致性？
- 方法与思路
- 作者分别处理完整响应、加权调整和类别内插补，提出使用调整后插补值的刀切方差估计及相应线性化形式。
- 材料陈述的贡献
- 摘要称在残差正则条件及类别内均匀响应假设下建立无响应情形的一致性，并展示加权均值与随机热卡插补的模拟。
- 阅读关注点
- 应核对后分层与加权类别交叉时的处理、插补值调整方法、残差条件和均匀响应假设，以及模拟如何评估方差估计。
- 阅读边界
- 来源为未注明稿件版本的OpenAlex索引摘要。一致性依赖所述条件；摘要未列出条件细节，不能推广到任意类别内响应机制或插补方法。
原文摘要
Poststratified estimators are commonly used in sample surveys to improve the efficiency of estimators and to ensure calibration to known poststrata counts. Similarly, generalized regression estimators are used to handle two or more poststratifiers with known marginal counts. In addition, weighting adjustment within weighting classes is used to handle unit nonresponse, and imputation within imputation classes is used to handle item nonresponse. For the full response case, asymptotic consistency of the jackknife variance estimator under stratified multistage sampling is established using mild regularity conditions on “residuals” similar to those of Scott and Wu for ratio and regression estimation under simple random sampling. A jackknife linearization variance estimator, obtained by linearizing the jackknife variance estimator, is also given. For unit nonresponse, the general case of poststrata cutting across weighting classes is considered, and a jackknife variance estimator and the corresponding jackknife linearization variance estimator are obtained. For item nonresponse, weighted mean imputation and weighted hot deck stochastic imputation within imputation classes are studied. Jackknife variance estimators, based on “adjusted” imputed values, are proposed, and the corresponding jackknife linearization variance estimators are obtained. Asymptotic consistency of the jackknife variance estimator is established for both the unit and item nonresponse cases under mild conditions on “residuals,” assuming uniform response within classes. Simulation results for the poststratified estimator under weighted mean imputation and weighted hot deck stochastic imputation are presented.