{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:73BGC46YQI4DM6FCBITWMD4MOI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3bf6f5c0b9f7a1684f235afec16c70412ebf501f3950e18f8c899c70e1be5b95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-13T14:20:22Z","title_canon_sha256":"098075f51b03168f439a9e170d68d9ef06ab4754c40f328bb7c094336c6c4a57"},"schema_version":"1.0","source":{"id":"1607.03752","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03752","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03752v2","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03752","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"73BGC46YQI4D","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"73BGC46YQI4DM6FC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"73BGC46Y","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:a3c2b0b38ec1403333c2bfb57abcdb261baa44408e270ae05e3c6894876b2509","target":"graph","created_at":"2026-05-18T00:23:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate nonparametric regression methods based on spatial depth and quantiles when the response and the covariate are both functions. As in classical quantile regression for finite dimensional data, regression techniques developed here provide insight into the influence of the functional covariate on different parts, like the center as well as the tails, of the conditional distribution of the functional response. Depth and quantile based nonparametric regressions are useful to detect heteroscedasticity in functional regression. We derive the asymptotic behaviour of nonparametric depth a","authors_text":"Joydeep Chowdhury, Probal Chaudhuri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-13T14:20:22Z","title":"Nonparametric Depth and Quantile Regression for Functional Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03752","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d49ea5a345e9e566bc325cc0a9ba6670003b6caae3c6245c39cad3ac95a72440","target":"record","created_at":"2026-05-18T00:23:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3bf6f5c0b9f7a1684f235afec16c70412ebf501f3950e18f8c899c70e1be5b95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-13T14:20:22Z","title_canon_sha256":"098075f51b03168f439a9e170d68d9ef06ab4754c40f328bb7c094336c6c4a57"},"schema_version":"1.0","source":{"id":"1607.03752","kind":"arxiv","version":2}},"canonical_sha256":"fec26173d882383678a20a27660f8c720b9268d0131c218d45a90a14dea44350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fec26173d882383678a20a27660f8c720b9268d0131c218d45a90a14dea44350","first_computed_at":"2026-05-18T00:23:46.133223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:46.133223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0J0CDAjsbEGZmgkt11IBU2yzATzDbbrzhE5PZJS02x0sN9ztpRv8FDo968xoNPPwKsc941hAMQ+xpyZSD6k7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:46.133767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03752","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d49ea5a345e9e566bc325cc0a9ba6670003b6caae3c6245c39cad3ac95a72440","sha256:a3c2b0b38ec1403333c2bfb57abcdb261baa44408e270ae05e3c6894876b2509"],"state_sha256":"6b38e08afdbbad879541ef00d3840e7ee7b536762e28bae08b0b852ae46c647c"}