{"paper":{"title":"Conditional regularized halfspace depth for sparse functional data and its applications","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Hyemin Yeon, Sara Lopez-Pintado, Xiongtao Dai","submitted_at":"2026-05-20T01:48:32Z","abstract_excerpt":"Many functional datasets are observed sparsely and irregularly. Ordering such data is challenging because only limited information is available from each observation, while the underlying trajectories remain infinite-dimensional. This paper develops a novel depth notion for sparse functional data, called the conditional regularized halfspace depth (CRHD). CRHD is defined as the infimum of conditional halfspace probabilities of the underlying trajectory given the observed sparse measurements, thereby enabling depth evaluation directly at sparse observations without requiring trajectory reconstr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20604","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20604/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"}