Primary Submission Category: Weighting
Generalized Entropy Calibration for Inference with Partially Observed Data: A Unified Framework
Authors: Mst Moushumi Pervin, Hengfang Wang, Jae Kwang Kim,
Presenting Author: Mst Moushumi Pervin*
Missing data is an universal problem in statistics. We develop a unified frame-
work for estimating parameters defined by general estimating equations under a
missing-at-random (MAR) mechanism, based on generalized entropy calibration
weighting. We construct weights by minimizing a convex entropy subject to (i) bal-
ancing constraints on a data-adaptive calibration function, estimated using flexible
machine-learning predictors with cross-fitting, and (ii) a debiasing constraint involv-
ing the fitted propensity score (PS) model. The resulting estimator is doubly robust,
remaining consistent if either the outcome regression (OR) or the PS model is cor-
rectly specified, and attains the semiparametric efficiency bound when both models
are correctly specified. Our formulation encompasses classical inverse probability
weighting (IPW) and augmented IPW (AIPW) as special cases and accommodates
a broad class of entropy functions. We illustrate the versatility of the approach in
three important settings: semi-supervised learning with unlabeled outcomes, regres-
sion analysis with missing covariates, and causal effect estimation in observational
studies. Extensive simulation studies and real-data applications demonstrate that
the proposed estimators achieve greater efficiency and numerical stability than exist-
ing methods. In particular, the proposed estimator outperforms the classical AIPW
estimator under the OR model misspecification.