Doubly Robust Estimation and Semiparametric Efficiency in Generalized Partially Linear Models with Missing Outcomes

Lu Wang (), Zhongzhe Ouyang and Xihong Lin
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Lu Wang: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA
Zhongzhe Ouyang: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA
Xihong Lin: Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA

Stats, 2024, vol. 7, issue 3, 1-20

Abstract: We investigate a semiparametric generalized partially linear regression model that accommodates missing outcomes, with some covariates modeled parametrically and others nonparametrically. We propose a class of augmented inverse probability weighted (AIPW) kernel–profile estimating equations. The nonparametric component is estimated using AIPW kernel estimating equations, while parametric regression coefficients are estimated using AIPW profile estimating equations. We demonstrate the doubly robust nature of the AIPW estimators for both nonparametric and parametric components. Specifically, these estimators remain consistent if either the assumed model for the probability of missing data or that for the conditional mean of the outcome, given covariates and auxiliary variables, is correctly specified, though not necessarily both simultaneously. Additionally, the AIPW profile estimator for parametric regression coefficients is consistent and asymptotically normal under the semiparametric model defined by the generalized partially linear model on complete data, assuming that the missing data mechanism is missing at random. When both working models are correctly specified, this estimator achieves semiparametric efficiency, with its asymptotic variance reaching the efficiency bound. We validate our approach through simulations to assess the finite sample performance of the proposed estimators and apply the method to a study that investigates risk factors associated with myocardial ischemia.

Keywords: asymptotics; augmented inverse probability weighting; kernel smoothing; missing data at random; profile-kernel estimating equation; semiparametric efficiency (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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