{"paper":{"title":"Rates of convergence in conditional covariance matrix with nonparametric entries estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Clement Marteau, Jean-Michel Loubes, Maikol Sol\\'is","submitted_at":"2013-10-30T17:50:37Z","abstract_excerpt":"Let $X\\in \\mathbb{R}^p$ and $Y\\in \\mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\\mathrm{Cov}\\left(\\mathrm{E}\\left[\\boldsymbol{X}\\vert Y\\right]\\right)$ applying a plug-in kernel-based algorithm to its entries. Next, we investigate the estimators rate of convergence under smoothness hypotheses on the density function of $(\\boldsymbol{X},Y)$. In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the $\\mathrm{Cov}\\left(\\mathrm{E}\\left[\\boldsymbol{X}\\vert Y\\right]\\right)$ entries. We illust"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8244","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"}