{"paper":{"title":"On predictive density estimation with additional information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Abdolnasser Sadeghkhani, \\'Eric Marchand","submitted_at":"2017-09-22T14:32:51Z","abstract_excerpt":"Based on independently distributed $X_1 \\sim N_p(\\theta_1, \\sigma^2_1 I_p)$ and $X_2 \\sim N_p(\\theta_2, \\sigma^2_2 I_p)$, we consider the efficiency of various predictive density estimators for $Y_1 \\sim N_p(\\theta_1, \\sigma^2_Y I_p)$, with the additional information $\\theta_1 - \\theta_2 \\in A$ and known $\\sigma^2_1, \\sigma^2_2, \\sigma^2_Y$. We provide improvements on benchmark predictive densities such as plug-in, the maximum likelihood, and the minimum risk equivariant predictive densities. Dominance results are obtained for $\\alpha-$divergence losses and include Bayesian improvements for re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07778","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":""},"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"}