{"id":"W3093563453","doi":"10.5539/ijsp.v9n6p108","title":"Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs","year":2020,"lang":"en","type":"article","venue":"International Journal of Statistics and Probability","topic":"Advanced Statistical Methods and Models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Positive-definite matrix; Covariance; Applied mathematics; Estimator; Least-squares function approximation; Covariance matrix; Estimation of covariance matrices; Combinatorics; Statistics; Eigenvalues and eigenvectors","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003934206,0.0001006344,0.000314401,0.00002169359,0.00004338823,0.00001994245,0.0001726708,0.00003354688,0.00001873094],"category_scores_gemma":[0.003564894,0.00006994708,0.00004992812,0.0000533966,0.0001646859,0.00008926389,0.00007664497,0.0001211517,1.860091e-8],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001792548,"about_ca_system_score_gemma":0.00007600033,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000110125,"about_ca_topic_score_gemma":0.000009812984,"domain_scores_codex":[0.9987047,0.0001293976,0.0006909723,0.0001270558,0.0002664447,0.00008144214],"domain_scores_gemma":[0.9965796,0.001548721,0.0007815941,0.00008882807,0.0009305974,0.00007061196],"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":[0.0002389478,0.00006497979,0.001379401,0.0002826311,0.00009601639,9.301027e-7,0.0006387113,0.000201468,0.008894334,0.9832041,0.00004236931,0.004956121],"study_design_scores_gemma":[0.0007442434,0.0001533424,0.002468078,0.00006199857,0.00006629245,0.00001164842,0.00004926074,0.007381926,0.002764072,0.9860249,0.0001993693,0.00007487785],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1769469,0.0000503565,0.8159837,0.0006679774,0.0001186627,0.0001906311,0.00602853,0.000001995707,0.00001119639],"genre_scores_gemma":[0.4414048,0.00003842678,0.5583996,0.00006956226,0.00006778985,0.000002101552,0.000007017077,0.000005583453,0.00000511081],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2644579,"threshold_uncertainty_score":0.4267769,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1107821168136998,"score_gpt":0.4265200669770371,"score_spread":0.3157379501633373,"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."}}