{"paper":{"title":"Goodness-of-Fit Testing for Point Processes in Large Populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A unitary transformation maps the natural testing process for parametric point processes to a limiting target whose distribution is free of unknown intensity parameters.","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Estate V. Khmaladze, Roger J. A. Laeven, Sami Umut Can","submitted_at":"2026-05-15T10:09:49Z","abstract_excerpt":"Suppose we have an observed path from a point process counting event occurrences in a large population. Based on the observed path, we would like to test the null hypothesis that the conditional intensity of the point process belongs to a particular parametric family. We propose a novel approach to conducting such goodness-of-fit tests. The idea is to construct a unitary transformation of a natural parametric testing process such that it converges weakly to a ``standard'' target process, independent of the particular parametric form assumed under the null hypothesis. This transformation theref"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a novel approach to conducting such goodness-of-fit tests. The idea is to construct a unitary transformation of a natural parametric testing process such that it converges weakly to a ``standard'' target process, independent of the particular parametric form assumed under the null hypothesis. This transformation therefore paves the way for asymptotically distribution-free goodness-of-fit testing of parametric point processes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that a unitary transformation exists which maps the natural parametric testing process to a limiting target whose distribution is completely free of the unknown parameters in the intensity family; this premise is invoked when the abstract states that the transformed process converges weakly to a standard target independent of the parametric form.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A unitary transformation is introduced for parametric testing processes in point processes to enable asymptotically distribution-free goodness-of-fit tests.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A unitary transformation maps the natural testing process for parametric point processes to a limiting target whose distribution is free of unknown intensity parameters.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b1bf411d1d85b30d1c992ab6baf50564dad19f208435fe66375f359d5f7eb274"},"source":{"id":"2605.15814","kind":"arxiv","version":1},"verdict":{"id":"91f67521-fde8-4ba2-94bd-56515967fac9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:42:32.873412Z","strongest_claim":"We propose a novel approach to conducting such goodness-of-fit tests. 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