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arXiv · 2509.15846

Doubly Robust Estimation of Continuous Outcomes under Multiple Treatment Levels via GPS, CBPS, and Penalized Empirical Likelihood

Byeonghee Lee·Joonsung Kang
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Abstract

This paper develops a unified framework for estimating continuous outcomes under multiple treatment levels in observational studies. We integrate the Generalized Propensity Score (GPS), Covariate Balancing Propensity Score (CBPS), and outcome regression into a Penalized Empirical Likelihood (PEL) formulation. The GPS is parameterized by $\boldsymbol{\beta}$ and denoted $\pi_{\boldsymbol{\beta}}(\mathbf{X})$, while CBPS imposes moment conditions to ensure covariate balance. Outcome regression flexibly models the continuous response $Y$, and doubly robust estimation ensures consistency under either correct model specification. PEL allows simultaneous estimation and variable selection using general estimating equations. Simulation results and comparisons with state-of-the-art meta-learners confirm the effectiveness of our method.

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Byeonghee Lee, Joonsung Kang. 2025-09-19. Doubly Robust Estimation of Continuous Outcomes under Multiple Treatment Levels via GPS, CBPS, and Penalized Empirical Likelihood. https://arxiv.org/abs/2509.15846

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