{"paper":{"title":"Minimax theory of estimation of linear functionals of the deconvolution density with or without sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marianna Pensky","submitted_at":"2014-11-06T16:48:21Z","abstract_excerpt":"The present paper considers a problem of estimating a linear functional $\\Phi=\\int_{-\\infty}^\\infty \\varphi(x) f(x)dx$ of an unknown deconvolution density $f$ on the basis of i.i.d. observations $Y_i = \\theta_i + \\xi_i$ where $\\xi_i$ has a known pdf $g$ and $f$ is the pdf of $\\theta_i$. Although various aspects and particular cases of this problem have been treated by a number of authors, there are still many gaps. In particular, there are no minimax lower bounds for an estimator of $\\Phi$ for an arbitrary function $\\varphi$. The general upper risk bounds cover only the case when the Fourier t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1660","kind":"arxiv","version":3},"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"}