{"paper":{"title":"Polynomial Maximization Method with Fractional Polynomial Basis: A Frequentist Bridge to Bayesian Fractional Polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"PMM-FP extends polynomial maximization to fractional bases and delivers a closed-form variance-reduction factor of 1 minus gamma_3 squared over 2 plus gamma_4 relative to ordinary least squares for asymmetric non-Gaussian errors.","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Serhii Zabolotnii","submitted_at":"2026-05-16T07:07:26Z","abstract_excerpt":"Fractional polynomials are widely used for dose-response modelling, and recent Bayesian fractional polynomial work has renewed interest in this finite model class. We propose PMM-FP, a frequentist extension of Kunchenko's polynomial maximization method to fractional-polynomial bases, developed in two parallel tracks for positive and full FP power sets under appropriate moment conditions. The main result is the closed-form variance-reduction coefficient g_2=1-gamma_3^2/(2+gamma_4) relative to OLS-FP for asymmetric non-Gaussian errors, formalised in Lean 4 and validated by Monte Carlo. On GBSG r"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The main result is the closed-form variance-reduction coefficient g_2=1-gamma_3^2/(2+gamma_4) relative to OLS-FP for asymmetric non-Gaussian errors, formalised in Lean 4 and validated by Monte Carlo.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The extension to fractional-polynomial bases is developed under appropriate moment conditions for the positive and full FP power sets.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"PMM-FP extends polynomial maximization to fractional polynomial bases and derives a closed-form variance-reduction coefficient g2 for asymmetric non-Gaussian errors, formalized in Lean 4 and checked via Monte Carlo.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"PMM-FP extends polynomial maximization to fractional bases and delivers a closed-form variance-reduction factor of 1 minus gamma_3 squared over 2 plus gamma_4 relative to ordinary least squares for asymmetric non-Gaussian errors.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8b7ef932c7c4f35b431aa039681db529b5108c66ac5c831e52101d662365df72"},"source":{"id":"2605.16846","kind":"arxiv","version":1},"verdict":{"id":"8a30210d-c340-4f65-8036-58ae9d16c866","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:26:28.378123Z","strongest_claim":"The main result is the closed-form variance-reduction coefficient g_2=1-gamma_3^2/(2+gamma_4) relative to OLS-FP for asymmetric non-Gaussian errors, formalised in Lean 4 and validated by Monte Carlo.","one_line_summary":"PMM-FP extends polynomial maximization to fractional polynomial bases and derives a closed-form variance-reduction coefficient g2 for asymmetric non-Gaussian errors, formalized in Lean 4 and checked via Monte Carlo.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The extension to fractional-polynomial bases is developed under appropriate moment conditions for the positive and full FP power sets.","pith_extraction_headline":"PMM-FP extends polynomial maximization to fractional bases and delivers a closed-form variance-reduction factor of 1 minus gamma_3 squared over 2 plus gamma_4 relative to ordinary least squares for asymmetric non-Gaussian errors."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16846/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:31:45.676913Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.123167Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.317873Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.390665Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"2c88d539bf96cb1a0e0f5ed0fe0e6a46353b33330a4126021e9a0c2c919faff8"},"references":{"count":30,"sample":[{"doi":"","year":2002,"title":"Kunchenko, Yuriy P. , title =. 2002 , isbn =","work_id":"b03aaa70-e8b6-4e23-b0f1-ae23f4aef6ce","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"and Warsza, Zygmunt L","work_id":"f14bbf9c-ec75-479f-883d-ff186cc041e7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"and Warsza, Zygmunt L","work_id":"fcbad252-194f-4b39-8571-3009e3a46f56","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Zabolotnii, Serhii and Tkachenko, Oleksandr and Warsza, Zygmunt L. , title =. Automation 2022: New Solutions and Technologies for Automation, Robotics and Measurement Techniques , series =. 2022 , doi","work_id":"461c1d19-d483-4851-b698-537a37c201f5","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Zabolotnii, Serhii and Tkachenko, Oleksandr and Warsza, Zygmunt L. , title =. Automation 2023: Key Challenges in Automation, Robotics and Measurement Techniques , series =. 2023 , doi =","work_id":"e9ba6a24-3146-44ff-b513-6291b9e9cef2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":30,"snapshot_sha256":"0a98fe86b1f5728a5d33f6e739f8eb3789628019d310585e6b1022c6f8418f3e","internal_anchors":3},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a455f65798a59b0ce3103f3a92b0241bf8fbff77064ef000fc0598677a107ab4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}