Inference with Imputed Conditional Means
基于条件均值填补数据的统计推断AI 解读 ↓
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基于条件均值填补数据的统计推断
- 研究问题
- 当缺失值已被填补模型的预测均值替代时，如何进行统计推断，并计入由缺失数据和填补模型带来的不确定性？
- 方法与思路
- 作者对点估计量和方差估计量作渐近展开，结合完整数据分析的组成部分与填补模型的两项汇总量，构造解析近似。
- 材料陈述的贡献
- 摘要将所得公式解释为无限次多重填补的一阶近似，并称适用时可减少计算负担及模拟误差，且便于向外部分析者提供必要信息。
- 阅读关注点
- 应核对两项汇总量的定义、填补与分析模型的匹配要求，以及独立同分布、单变量缺失和均值光滑函数条件之外的扩展。
- 阅读边界
- 仅据版本未注明的OpenAlex索引摘要。摘要未说明缺失机制和完整适用条件；一阶近似与减少模拟误差不等于任意情形下推断更准确。
原文摘要
In this article we present analytic techniques for inference from a dataset in which missing values have been replaced by predictive means derived from an imputation model. The derivations are based on asymptotic expansions of point estimators and their associated variance estimators, and the resulting formulas can be thought of as first-order approximations to standard multiple-imputation procedures with an infinite number of imputations for the missing values. Our method, where applicable, may require substantially less computational effort than creating and managing a multiply imputed database; moreover, the resulting inferences can be more precise than those derived from multiple imputation, because they do not rely on simulation. Our techniques use components of the standard complete-data analysis, along with two summary measures from the fitted imputation model. If the imputation and analysis phases are carried out by the same person or organization, then the method provides a quick assessment of the variability due to missing data. If a data producer is supplying the imputed data set to outside analysts, then the necessary summary measures could be supplied to the analysts, enabling them to apply the method themselves. We emphasize situations with iid samples, univariate missing data, and complete-data point estimators that are smooth functions of means, but also discuss extensions to more complicated situations. We illustrate properties of our methods in several examples, including an application to a large dataset on fatal accidents maintained by the National Highway Traffic Safety Administration.