Orthocomplement of Tangent Space for Semiparametric Markov Models
This study defines the orthogonal complement of the tangent space within semiparametric Markov models, encompassing graphical models governed by conditional independence constraints. The authors broaden established findings related to directed acyclic graphs (DAGs) to apply to general Markov models, which allows for the derivation of all influence functions pertinent to any target parameter. This advancement supports the efficient estimation of finite-dimensional parameters, yielding estimators that are asymptotically normal and consistent at a rate of root-n. The research offers a solid framework for developing both regular and asymptotically linear estimators through influence functions, essential for achieving statistically efficient inference in the social and empirical sciences.
Key facts
- Graphical models are Markov models defined using conditional independence restrictions.
- Semiparametric theory provides a framework for constructing regular and asymptotically linear estimators via influence functions.
- Characterizing all influence functions for a target parameter is crucial for efficient inference.
- For DAGs, the orthogonal complement of the tangent space is known.
- This paper extends the characterization to general Markov models.
- Estimators are asymptotically normal and root-n consistent.
- The work applies to social and empirical sciences.
- The paper is on arXiv with ID 2607.23439.
Entities
Institutions
- arXiv