{"id":"W1985720541","doi":"10.1016/j.jmva.2011.03.003","title":"Some tests for the covariance matrix with fewer observations than the dimension under non-normality","year":2011,"lang":"en","type":"article","venue":"Journal of Multivariate Analysis","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":62,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Identity matrix; Covariance matrix; Scatter matrix; Estimation of covariance matrices; Law of total covariance; Covariance; Matrix (chemical analysis); Dimension (graph theory); Normality; CMA-ES; Rational quadratic covariance function; Covariance function; Statistics; Applied mathematics; Combinatorics; Covariance intersection; Eigenvalues and eigenvectors","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001289586,0.0001455513,0.0003773886,0.0001097073,0.0004394175,0.00005316654,0.0004238469,0.00005524379,0.00003554351],"category_scores_gemma":[0.0001603195,0.00006279211,0.0004227576,0.000733422,0.0000620058,0.0002628019,0.00003895464,0.0001938517,0.000003702046],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003435049,"about_ca_system_score_gemma":0.00006395546,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003263981,"about_ca_topic_score_gemma":0.0001895771,"domain_scores_codex":[0.9987065,0.0000842451,0.0005816255,0.0001324195,0.0003128287,0.0001824448],"domain_scores_gemma":[0.9962947,0.001641495,0.0009683632,0.000502012,0.0005327212,0.00006070559],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"observational","study_design_scores_codex":[0.004015754,0.004762884,0.06130397,0.0003002289,0.05274705,0.00003095741,0.02083159,0.08610198,0.01192191,0.7430218,0.0133213,0.001640579],"study_design_scores_gemma":[0.005628246,0.000288925,0.6982267,0.00007972575,0.02590016,0.00004374151,0.002310293,0.09690341,0.001004327,0.166689,0.00241576,0.0005097267],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3179098,0.0002559422,0.6767608,0.004220368,0.00009910967,0.0006388773,0.0000378348,0.00001758417,0.00005974514],"genre_scores_gemma":[0.9388207,0.00007964624,0.06025674,0.0001332493,0.0002041271,0.00004150434,0.000002714785,0.00001758564,0.0004437293],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6369227,"threshold_uncertainty_score":0.3379689,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1077635713744592,"score_gpt":0.3521948851587209,"score_spread":0.2444313137842618,"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."}}