{"id":"W1534154518","doi":"10.1007/s11425-012-4434-7","title":"A strong approximation of self-normalized sums","year":2012,"lang":"en","type":"article","venue":"Science China Mathematics","topic":"Probability and Risk Models","field":"Decision Sciences","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Strassen algorithm; Independent and identically distributed random variables; Random variable; Sequence (biology); Combinatorics; Type (biology); Domain (mathematical analysis); Discrete mathematics; Mathematical analysis; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005376366,0.00146199,0.001735808,0.002487359,0.001061695,0.003564246,0.002850971,0.001981327,0.005097],"category_scores_gemma":[0.02431144,0.0008991337,0.001811784,0.001661278,0.00409099,0.006675413,0.00475295,0.004448878,0.0006129991],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001790715,"about_ca_system_score_gemma":0.001491552,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001135453,"about_ca_topic_score_gemma":0.0008553928,"domain_scores_codex":[0.9975348,0.001234942,0.00009570651,0.0003263773,0.0005662866,0.0002419726],"domain_scores_gemma":[0.9875043,0.008230944,0.0008179591,0.0009763433,0.001422721,0.001047792],"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":[0.00003978786,0.00003129091,0.0002973474,0.00005950998,0.00003456533,0.00005053327,0.00008296315,0.01862929,0.000601883,0.9751949,0.0009252857,0.004052537],"study_design_scores_gemma":[0.00001015397,0.00002642644,0.0001759603,0.0000228315,0.00001718131,0.00008167086,0.00003067071,0.2437133,0.0003061974,0.7545121,0.001087791,0.00001570077],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09297855,0.001667374,0.8781245,0.002098162,0.0004866622,0.00003501308,0.0001450444,0.0002515117,0.02421307],"genre_scores_gemma":[0.8602964,0.001799544,0.1028233,0.0008514595,0.0009954408,0.0001382382,0.0003046436,0.0002493798,0.03254158],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005376366,"threshold_uncertainty_score":0.02843332,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1089534748246716,"score_gpt":0.3881775318700271,"score_spread":0.2792240570453555,"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."}}