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These models belong to the broader class of Markov models, defined using solely conditional independence (CI) restrictions.\n  In order to estimate finite-dimensional target parameters in such models efficiently, semi-parametric theory provides a principled framework for constructing regular and asymptotically linear estimators via influence functions (IFs). These estimators are asymptotically normal and root-$n$ consistent. Characterizing the class of all influence functions for a target parameter is crucial for statistically efficient inference in these models.\n  For models that are Markov relative to directed acyclic graphs (DAGs), the orthogonal complement of the tangent space is known, implying that for any target the class of all influence functions can be derived once an influence function is obtained. On the other hand, for Mar","title":"A Characterization of the Orthocomplement of the Tangent Space of Semiparametric Markov Models","url":"https://arxiv.org/abs/2607.23439","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.23439v1 Announce Type: cross \nAbstract: Graphical models are ubiquitous in social and empirical science as they are intuitive and easy to use. These models belong to the broader class of Markov models, defined using solely conditional independence (CI) restrictions.\n  In order to estimate finite-dimensional target parameters in such models efficiently, semi-parametric theory provides a principled framework for constructing regular and asymptotically linear estimators via influence functions (IFs). These estimators are asymptotically normal and root-$n$ consistent. 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