{"id":"W4415683829","doi":"10.3390/axioms14110784","title":"The Law of the Iterated Logarithm for the Error Distribution Estimator in First-Order Autoregressive Models","year":2025,"lang":"en","type":"article","venue":"Axioms","topic":"Statistical Methods and Inference","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia, Okanagan Campus; University of British Columbia","funders":"National Natural Science Foundation of China","keywords":"Estimator; Law of the iterated logarithm; Autoregressive model; Kernel smoother; Asymptotic distribution; Kernel (algebra); STAR model; Iterated logarithm; Logarithm","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000431525,0.00009177258,0.0001456215,0.000009340025,0.000297627,0.00003765773,0.0002882906,0.00005959797,0.00001098083],"category_scores_gemma":[0.002726512,0.00003867703,0.00005313706,0.0002147391,0.000255827,0.00003457496,0.00008073943,0.0001208002,9.988506e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003300711,"about_ca_system_score_gemma":0.00005385752,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001389855,"about_ca_topic_score_gemma":0.0001957924,"domain_scores_codex":[0.9992463,0.00009329613,0.000262576,0.0001175341,0.0001153739,0.0001649461],"domain_scores_gemma":[0.9950669,0.004307037,0.0001049732,0.0003318036,0.0001746208,0.00001461627],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002387802,0.00003311542,0.0000168731,0.00003330227,0.00002156035,2.586524e-7,0.0002573336,0.000142653,0.00001398156,0.9954858,0.0008869486,0.003084319],"study_design_scores_gemma":[0.0002286586,0.00001609046,0.0007989645,0.000107969,0.00002880735,4.537504e-7,0.0001334335,0.4469881,0.0003804808,0.5504723,0.000803504,0.00004129859],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.002963583,0.0001342196,0.9916813,0.003480106,0.0002588314,0.0005800942,0.0001554978,0.0000152238,0.0007311202],"genre_scores_gemma":[0.9817954,0.000008188176,0.01739938,0.0001487265,0.00001565406,0.0001856974,0.000006104569,0.000008339557,0.0004324612],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9788319,"threshold_uncertainty_score":0.3264087,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06678281259858174,"score_gpt":0.3810592339779725,"score_spread":0.3142764213793907,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}