{"paper":{"title":"A Class of Higher-Order INAR Random Fields for Poisson Counts and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Angelika Silbernagel, Christian H. Wei{\\ss}","submitted_at":"2026-05-14T13:06:16Z","abstract_excerpt":"Existing integer-valued autoregressive (INAR) models for count random fields suffer from difficulties in characterizing the stationary marginal distribution and in computing conditional probabilities (as required for likelihood inference). To overcome these drawbacks, the novel class of combined INAR (CINAR) models is proposed, which both exhibits the classical autoregressive dependence structure and allows to specify the marginal distribution within the wide class of discrete self-decomposable distributions. In particular, CINAR random fields can be equipped with a Poisson or negative-binomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14796","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}