Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions

• URL: http://arxiv.org/abs/2207.04771v2
• Date: Fri, 16 Feb 2024 13:48:47 GMT
• Title: Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions
• Authors: Heiner Kremer, Jia-Jie Zhu, Krikamol Muandet, Bernhard Sch\"olkopf
• Abstract summary: We propose a new estimation method based on generalized empirical likelihood (GEL) GEL provides a more general framework and has been shown to enjoy favorable small-sample properties compared to GMM-based estimators. We provide kernel- and neural network-based implementations of the estimator, which achieve state-of-the-art empirical performance on two conditional moment restriction problems.
• Score: 19.39005034948997
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional moment restrictions. Previous works addressed this problem by extending the generalized method of moments (GMM) to continuum moment restrictions. In contrast, generalized empirical likelihood (GEL) provides a more general framework and has been shown to enjoy favorable small-sample properties compared to GMM-based estimators. To benefit from recent developments in machine learning, we provide a functional reformulation of GEL in which arbitrary models can be leveraged. Motivated by a dual formulation of the resulting infinite dimensional optimization problem, we devise a practical method and explore its asymptotic properties. Finally, we provide kernel- and neural network-based implementations of the estimator, which achieve state-of-the-art empirical performance on two conditional moment restriction problems.

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