{"id":"W7109872849","doi":"","title":"Tracy-Widom, Gaussian, and Bootstrap:Approximations for Leading Eigenvalues in High-Dimensional PCA","year":2025,"lang":"en","type":"preprint","venue":"","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"Aarhus Universitets Forskningsfond; Deutsche Forschungsgemeinschaft; Aarhus Universitet","keywords":"Eigenvalues and eigenvectors; Dimension (graph theory); Sample size determination; Gaussian; Covariance matrix; Sample (material); Matrix (chemical analysis); Sample mean and sample covariance","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000441988,0.0002845367,0.0005626213,0.0002821803,0.0001636069,0.0001099023,0.0002315744,0.0002847981,0.00008979123],"category_scores_gemma":[0.0001673103,0.0002528851,0.0001532257,0.0001717193,0.00005431103,0.00007125131,0.0002336161,0.0003358877,0.00000646639],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006034502,"about_ca_system_score_gemma":0.0001486877,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001273828,"about_ca_topic_score_gemma":0.000165192,"domain_scores_codex":[0.998354,0.00004118249,0.0006434242,0.0005213531,0.0001753123,0.0002647655],"domain_scores_gemma":[0.99812,0.001068278,0.0002143704,0.0004413258,0.00008599213,0.00007004079],"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":[0.00004390481,0.0002778114,0.0001298596,0.001718466,0.0001022897,0.000001174012,0.0003859717,0.0006025333,0.0001167528,0.9787902,0.01485918,0.002971857],"study_design_scores_gemma":[0.001703456,0.0000187448,0.000467751,0.0003483767,0.0001645184,0.000003730602,0.0001254507,0.02033887,0.0004679158,0.9729486,0.003022953,0.000389709],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.4220934,0.001988001,0.4869212,0.01631261,0.0009489033,0.01382297,0.001951574,0.0008512172,0.05511009],"genre_scores_gemma":[0.4676541,0.0002447175,0.5015447,0.0002510496,0.0002906553,0.003124139,0.0003089648,0.0000671329,0.02651459],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.04556069,"threshold_uncertainty_score":0.9999923,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0779822425594637,"score_gpt":0.3713245415945375,"score_spread":0.2933422990350738,"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."}}