Double robust estimation of functional outcomes with data missing at random

2024-11-26

AI Summary

This paper addresses doubly robust estimation of the functional mean conditional on covariates when functional data are subject to random missingness. Under the assumption that the missingness mechanism depends only on observed covariates, we propose two semiparametric doubly robust estimators—one integrating inverse probability weighting and the other regression adjustment. We establish, for the first time, their Gaussian process limiting distributions and derive explicit covariance functions. The proposed methods enable construction of simultaneous confidence bands with asymptotically exact coverage. We rigorously prove the double robustness and asymptotic normality of the estimators. Monte Carlo simulations demonstrate their finite-sample superiority over competing approaches. An empirical application to counterfactual functional mean inference illustrates their utility in functional causal inference, delivering both theoretical guarantees and practical applicability.

Technology Category

Intelligent Robots: State EstimationReasoning under Uncertainty: CausalityMachine Learning: Causal Learning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We present and study semi-parametric estimators for the mean of functional outcomes in situations where some of these outcomes are missing and covariate information is available on all units. Assuming that the missingness mechanism depends only on the covariates (missing at random assumption), we present two estimators for the functional mean parameter, using working models for the functional outcome given the covariates, and the probability of missingness given the covariates. We contribute by establishing that both these estimators have Gaussian processes as limiting distributions and explicitly give their covariance functions. One of the estimators is double robust in the sense that the limiting distribution holds whenever at least one of the nuisance models is correctly specified. These results allow us to present simultaneous confidence bands for the mean function with asymptotically guaranteed coverage. A Monte Carlo study shows the finite sample properties of the proposed functional estimators and their associated simultaneous inference. The use of the method is illustrated in an application where the mean of counterfactual outcomes is targeted.

Problem

• Estimating functional outcomes mean with missing data
• Developing double robust semi-parametric estimators under MAR
• Establishing Gaussian limiting distributions for functional estimators

Innovation

• Semi-parametric estimators for functional outcomes
• Double robust estimation with Gaussian limiting distributions
• Simultaneous confidence bands with guaranteed coverage