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Toward a Semiparametric Efficiency Theory under Equality Constraints in Nested Markov Models

arXiv · AI, language, vision and robotics · article · Aug 25, 2026 · UTC

Probabilistic models of Directed Acyclic Graphs (DAGs) with latent variables impose equality constraints on the observed data distribution beyond ordinary conditional independencies. These so-called Verma constraints arise in nested Markov models associated with Acyclic Directed Mixed Graphs, the latent projection of latent-variable DAGs. While nested Markov models have been extensively studied from the perspectives of graphical representation and causal identification, their implications for semiparametric efficiency theory remain less understood. We develop results toward establishing a semi

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