{"paper":{"title":"On Linear Regression for Interval-valued Data in $\\mathcal{K}_{\\mathcal{C}}\\left(\\mathbb{R}\\right)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Chunyang Li, Yan Sun","submitted_at":"2014-01-08T21:23:15Z","abstract_excerpt":"It has been some time since interval-valued linear regression was investigated. In this paper, we focus on linear regression for interval-valued data within the framework of random sets. The model we propose generalizes a series of existing models. We establish important properties of the model in the space of compact convex subsets of $\\mathbb{R}$, analogous to those for the classical linear regression. Furthermore, we carry out theoretical investigations into the least squares estimation that is widely used in the literature. A simulation study is presented that supports our theorems. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1831","kind":"arxiv","version":4},"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"}