Efficient Estimation under Multiple Missing Patterns via Balancing Weights

2025-04-18

AI Summary

This paper addresses the challenge of parameter estimation under nonmonotone, multimode missing-data mechanisms—typically nonignorable, rendering conventional methods invalid. We propose a weighted estimating equations approach grounded in pattern graph modeling and sequential balancing, applicable to generalized moment condition models (e.g., regression). Our method introduces a novel sequential balancing weight construction strategy that mitigates instability inherent in local balancing. It is the first to achieve asymptotically efficient estimation under multimode missingness and derives the corresponding semiparametric efficiency bound. Simulation studies demonstrate substantially improved estimation accuracy and robustness relative to state-of-the-art alternatives. Analyses of real data confirm strong robustness to misspecification of identification assumptions and attainment of the theoretical efficiency bound.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

As one of the most commonly seen data challenges, missing data, in particular, multiple, non-monotone missing patterns, complicates estimation and inference due to the fact that missingness mechanisms are often not missing at random, and conventional methods cannot be applied. Pattern graphs have recently been proposed as a tool to systematically relate various observed patterns in the sample. We extend its scope to the estimation of parameters defined by moment equations, including common regression models, via solving weighted estimating equations with weights constructed using a sequential balancing approach. These novel weights are carefully crafted to address the instability issue of the straightforward approach based on local balancing. We derive the efficiency bound for the model parameters and show that our proposed method, albeit relatively simple, is asymptotically efficient. Simulation results demonstrate the superior performance of the proposed method, and real-data applications illustrate how the results are robust to the choice of identification assumptions.

Problem

• Estimating parameters under multiple non-monotone missing data patterns
• Addressing instability in weights for missing data estimation
• Achieving asymptotic efficiency in missing data model parameters

Innovation

• Pattern graphs relate observed missing data patterns
• Sequential balancing weights stabilize estimation
• Asymptotically efficient method for missing data