{"paper":{"title":"Efficient estimation of conditional covariance matrices for dimension reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Jean-Michel Loubes, Maikol Sol\\'is, S\\'ebastien Da Veiga","submitted_at":"2011-10-14T15:12:15Z","abstract_excerpt":"Let $\\boldsymbol{X}\\in \\mathbb{R}^p$ and $Y\\in \\mathbb{R}$. In this paper we propose an estimator of the conditional covariance matrix, $\\mathrm{Cov}(\\mathbb{E}[\\boldsymbol{X}\\vert Y])$, in an inverse regression setting. Based on the estimation of a quadratic functional, this methodology provides an efficient estimator from a semi parametric point of view. We consider a functional Taylor expansion of $\\mathrm{Cov}(\\mathbb{E}[\\boldsymbol{X}\\vert Y])$ under some mild conditions and the effect of using an estimate of the unknown joint distribution. The asymptotic properties of this estimator are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3238","kind":"arxiv","version":4},"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"}