广义线性回归中协变量完全缺失时的双重稳健目标推断
Doubly robust target inference for generalized linear regression with completely missing covariates
浏览论文内容
中文总结 AI 辅助
针对目标数据协变量完全缺失的广义线性回归，提出双重稳健迁移学习框架，结合重要性加权与插补，实现一致且有效的目标总体推断。
中文摘要 AI 辅助
大规模多用途队列研究和生物样本库常常缺少特定下游分析所需的协变量。我们研究当关键协变量在目标数据中完全缺失但在相关源群体中可观测时，广义线性回归的目标总体推断问题。标准缺失协变量方法不能直接应用，因为它们要求目标总体中协变量至少部分可观测。我们在子总体偏移假设下开发了一个双重稳健的迁移学习框架，该假设允许不同总体间观测结果和协变量的分布不同，同时要求给定观测变量时缺失协变量的条件分布在总体间共享。与线性回归不同，非线性目标估计方程需要缺失协变量的参数索引条件泛函，而非固定的低阶条件矩集合。我们的估计器将重要性加权的源估计方程与这些条件泛函的插补相结合。在识别假设下，当密度比模型或条件协变量模型之一被正确指定时，估计器保持一致。在正则条件下，它是根号n一致且渐近正态的，并且当两个干扰模型都被正确指定时，达到半参数效率界。
英文摘要
Large-scale multipurpose cohort studies and biobanks often omit covariates needed for specific downstream analyses. We study target-population inference for generalized linear regression when key covariates are completely absent from the target data but observed in a related source population. Standard missing covariate methods are not directly applicable because they require at least partial observation of the covariates in the target population. We develop a doubly robust transfer learning framework under a sub-population shift assumption, which allows the distribution of the observed outcome and covariates to differ between populations while requiring the conditional distribution of the missing covariates given the observed variables to be shared. Unlike linear regression, nonlinear target estimating equations require parameter-indexed conditional functionals of the missing covariates rather than a fixed collection of low-order conditional moments. Our estimator combines importance-weighted source estimating equations with imputation of these conditional functionals. Under the identifying assumption, the estimator remains consistent when either the density-ratio model or the conditional-covariate model is correctly specified. Under regularity conditions, it is root-$n$ consistent and asymptotically normal, and attains the semiparametric efficiency bound when both nuisance models are correctly specified.
发表机构
- School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）
- Department of Statistics and Data Science, Tsinghua University（清华大学统计与数据科学系）
机构由 AI 辅助整理，请以论文原文为准。
