Variance Estimation for Survey Data with Composite Imputation and Nonnegligible Sampling Fractions
针对调查数据中非响应被插补且抽样分数不可忽略的情况，提出一种基于方差分解的方差估计方法，适用于复合插补（如冷库法和比率法组合），并通过美国人口普查局交通年度调查示例说明。
Abstract This article considers variance estimation for Horvitz–Thompson–type estimated totals based on survey data with imputed non-respondents and with nonnegligible sampling fractions. A method based on a variance decomposition is proposed. Our method can be applied to complicated situations where a composite of some deterministic and/or random imputation methods is used, including using imputed data in subsequent imputations. Although here linearization or Taylor expansion–type techniques are adopted, replication methods such as the jackknife, balanced repeated replication, and random groups can also be used in applying our method to derive variance estimators. Using our method, variance estimators can be derived under either the customary design-based approach or the model-assisted approach, and are asymptotically unbiased and consistent. The Transportation Annual Survey conducted at the U.S. Census Bureau, in which nonrespondents are imputed using a composite of cold deck and ratio type imputation methods, is used as an example as well as the motivation for our study.