Recursive-Head Geometry and Order-Free Efficient Inference in Finite-State Nested Markov Models

Haoyu Wei

Papers from arXiv.org

Abstract: Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither mb-shieldedness nor a district order. Exact counterexamples show that observational centering and kernel normalization alone do not certify tangency. For the node, complete-source edge, and compatible path-specific intervention targets considered here, boundary substitution yields a normalized configured active law and an order-free canonical-gradient formula, extended to finite mixtures by independent source redraws. A coherent one-step estimator with an exact remainder identity and a model-valid chart-flow targeted maximum likelihood estimator are efficient under stated local conditions. On a narrower source-isolated fixed-node subclass, a sequential estimator has an exact transition-factorized drift and up to $2^m$ nuisance-correctness regimes over $m$ active-district transitions; its all-correct influence function projects onto the canonical gradient, and an exact rational law exhibits a strict variance gap. These results separate order-free efficiency on arbitrary finite-state ADMGs from multiple robustness of a narrower construction.

Date: 2026-09
References: Add references at CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2609.17939 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2609.17939

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().