{"paper":{"title":"Convergence of Estimative Density to Information Projection for Misspecified Normal Distribution Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Yo Sheena","submitted_at":"2026-07-25T08:06:09Z","abstract_excerpt":"This paper investigates the convergence of an estimative multivariate normal density when the true distribution is a misspecified multivariate t-distribution. The statistical model is the family of k-dimensional normal distributions (N_k(\\mu,\\Sigma)), whereas the observations are assumed to follow (t_k(0,I_k,\\nu)), with (\\nu>6). The information projection of the true distribution onto the normal model is first identified as the normal distribution with mean zero and covariance matrix (\\nu/(\\nu-2)I_k).\n  The main objective is to evaluate the expected Kullback-Leibler divergence between this inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23092","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23092/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}