{"paper":{"title":"Exact Likelihood Inference and Robust Filtering for Gauss-Cauchy Convolution Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Exact analytical expressions for the Gauss-Cauchy convolution density enable stable maximum likelihood estimation and robust filtering in state-space models.","cross_cats":["stat.ME"],"primary_cat":"econ.EM","authors_text":"Chen Tong, Peter Reinhard Hansen","submitted_at":"2026-05-03T01:34:26Z","abstract_excerpt":"The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, Fisher information, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations. The conditional expectation of the latent Gaussian component is governed by a redescending location scor"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive analytical expressions for its density, score, Hessian, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The measurement noise follows exactly the Gauss-Cauchy convolution distribution and the scaled complementary error function remains numerically stable across all relevant parameter values encountered in estimation and filtering.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact analytical likelihood inference and a redescending robust filter are derived for Gauss-Cauchy convolution models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Exact analytical expressions for the Gauss-Cauchy convolution density enable stable maximum likelihood estimation and robust filtering in state-space models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"31d206e6f49752c71b096ea0f66f168f8b668a76564e2ff4107287d6a19285d0"},"source":{"id":"2605.01665","kind":"arxiv","version":2},"verdict":{"id":"05e6a10c-8cca-4f8a-97f0-2436b29691cc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T16:59:11.640253Z","strongest_claim":"We derive analytical expressions for its density, score, Hessian, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations.","one_line_summary":"Exact analytical likelihood inference and a redescending robust filter are derived for Gauss-Cauchy convolution models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The measurement noise follows exactly the Gauss-Cauchy convolution distribution and the scaled complementary error function remains numerically stable across all relevant parameter values encountered in estimation and filtering.","pith_extraction_headline":"Exact analytical expressions for the Gauss-Cauchy convolution density enable stable maximum likelihood estimation and robust filtering in state-space models."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01665/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T17:38:33.427029Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T05:01:23.545538Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:06:44.360130Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f0d03eeb676699fc193f6a3afdceee041f3a17516db1ba01c00298679a431d10"},"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"}