{"paper":{"title":"The RKHS Approach to Minimum Variance Estimation Revisited: Variance Bounds, Sufficient Statistics, and Exponential Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander Jung, Franz Hlawatsch, Sebastian Schmutzhard","submitted_at":"2012-10-24T13:20:36Z","abstract_excerpt":"The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a geometric formulation of five known lower bounds on the estimator variance (Barankin bound, Cramer-Rao bound, constrained Cramer-Rao bound, Bhattacharyya bound, and Hammersley-Chapman-Robbins bound) in terms of orthogonal projections onto a subspace of the RKHS associated with a given MVE problem. We show that, under mild conditions, the Barankin bound (the tightes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6516","kind":"arxiv","version":2},"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"}