{"paper":{"title":"Truncated Linear Models for Functional Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Giles Hooker, Peter Hall","submitted_at":"2014-06-30T13:41:26Z","abstract_excerpt":"A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\\int_I b(t)X(t)dt+\\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function and $I=[0, \\alpha]$ is a compact interval. However, in some problems the support of $b$ or $X$, $I_1$ say, is a proper and unknown subset of $I$, and is a quantity of particular practical interest. In this paper, motivated by a real-data example involving particulate emissions, we develop methods for estimating $I_1$. We give particular emphasis to the case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7732","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"}