A Versatile Estimation Procedure Without Estimating the Nonignorable Missingness Mechanism

Abstract

We consider the estimation problem in a regression setting where the outcome variable is subject to nonignorable missingness and identifiability is ensured by the shadow variable approach. We propose a versatile estimation procedure where modeling of missingness mechanism is completely bypassed. We show that our estimator is easy to implement and we derive the asymptotic theory of the proposed estimator. We also investigate some alternative estimators under different scenarios. Comprehensive simulation studies are conducted to demonstrate the finite sample performance of the method. We apply the estimator to a children’s mental health study to illustrate its usefulness.

Keywords:

• Asymptotic normality
• Identifiability
• Missingness mechanism
• Nonignorable missing data
• Semiparametric theory
• Shadow variable

Supplementary Materials

The supplementary materials contain all the detailed technical derivations and proofs.

Acknowledgments

The authors would like to thank the editor, an associate editor, and three reviewers for their insightful comments which have helped improve the manuscript substantially.

Additional information

Funding

This research was partially supported by the National Science Foundation under award numbers 1953526 and 2122074.