{"paper":{"title":"Inference on Directionally Differentiable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andres Santos, Zheng Fang","submitted_at":"2014-04-14T21:51:59Z","abstract_excerpt":"This paper studies an asymptotic framework for conducting inference on parameters of the form $\\phi(\\theta_0)$, where $\\phi$ is a known directionally differentiable function and $\\theta_0$ is estimated by $\\hat \\theta_n$. In these settings, the asymptotic distribution of the plug-in estimator $\\phi(\\hat \\theta_n)$ can be readily derived employing existing extensions to the Delta method. We show, however, that the \"standard\" bootstrap is only consistent under overly stringent conditions -- in particular we establish that differentiability of $\\phi$ is a necessary and sufficient condition for bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3763","kind":"arxiv","version":2},"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"}