{"paper":{"title":"Estimation of smooth functionals in high-dimensional models: bootstrap chains and Gaussian approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Vladimir Koltchinskii","submitted_at":"2020-11-07T15:13:56Z","abstract_excerpt":"Let $X^{(n)}$ be an observation sampled from a distribution $P_{\\theta}^{(n)}$ with an unknown parameter $\\theta,$ $\\theta$ being a vector in a Banach space $E$ (most often, a high-dimensional space of dimension $d$). We study the problem of estimation of $f(\\theta)$ for a functional $f:E\\mapsto {\\mathbb R}$ of some smoothness $s>0$ based on an observation $X^{(n)}\\sim P_{\\theta}^{(n)}.$ Assuming that there exists an estimator $\\hat \\theta_n=\\hat \\theta_n(X^{(n)})$ of parameter $\\theta$ such that $\\sqrt{n}(\\hat \\theta_n-\\theta)$ is sufficiently close in distribution to a mean zero Gaussian ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03789","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.03789/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}