{"paper":{"title":"Efficiency of Z-estimators indexed by the objective functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Fran\\c{c}ois Portier","submitted_at":"2015-09-15T06:17:07Z","abstract_excerpt":"We study the convergence of $Z$-estimators $\\widehat \\theta(\\eta)\\in \\mathbb R^p$ for which the objective function depends on a parameter $\\eta$ that belongs to a Banach space $\\mathcal H$. Our results include the uniform consistency over $\\mathcal H$ and the weak convergence in the space of bounded $\\mathbb R^p$-valued functions defined on $\\mathcal H$. Furthermore when $\\eta$ is a tuning parameter optimally selected at $\\eta_0$, we provide conditions under which an estimated $\\widehat \\eta$ can be replaced by $\\eta_0$ without affecting the asymptotic variance. Interestingly, these conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04413","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"}