{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SIEBN6QMNNFNTFJRKQAW6USTM3","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":"f7be68c08649446f9b17c91944a10be35dec0bd2c217d47707fcad778468d6fd","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-01-21T11:08:12Z","title_canon_sha256":"44e91c5dd06e8c92221c370cdeb160ba39a0cea59599ce4c0aac01154fd7e0b8"},"schema_version":"1.0","source":{"id":"1701.06009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06009","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06009v2","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06009","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"SIEBN6QMNNFN","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SIEBN6QMNNFNTFJR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SIEBN6QM","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:511ed5583c9510bdc237d6724f6758b87bec81875195a1ed5fc137ac8e5cf235","target":"graph","created_at":"2026-05-18T00:52:12Z","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":"The central subspace of a pair of random variables $(y,x) \\in \\mathbb{R}^{p+1}$ is the minimal subspace $\\mathcal{S}$ such that $y \\perp \\hspace{-2mm} \\perp x\\mid P_{\\mathcal{S}}x$. In this paper, we consider the minimax rate of estimating the central space of the multiple index models $y=f(\\beta_{1}^{\\tau}x,\\beta_{2}^{\\tau}x,...,\\beta_{d}^{\\tau}x,\\epsilon)$ with at most $s$ active predictors where $x \\sim N(0,I_{p})$. We first introduce a large class of models depending on the smallest non-zero eigenvalue $\\lambda$ of $var(\\mathbb{E}[x|y])$, over which we show that an aggregated estimator bas","authors_text":"Dongming Huang, Jun S. Liu, Qian Lin, Xinran Li","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-01-21T11:08:12Z","title":"On the optimality of sliced inverse regression in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06009","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:f4ce2ca8d833662bbb070e15984dfd7395cf8b9012aec59ffc69e6941debd57e","target":"record","created_at":"2026-05-18T00:52:12Z","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":"f7be68c08649446f9b17c91944a10be35dec0bd2c217d47707fcad778468d6fd","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-01-21T11:08:12Z","title_canon_sha256":"44e91c5dd06e8c92221c370cdeb160ba39a0cea59599ce4c0aac01154fd7e0b8"},"schema_version":"1.0","source":{"id":"1701.06009","kind":"arxiv","version":2}},"canonical_sha256":"920816fa0c6b4ad9953154016f525366d5a914d8a602130ee5fa211e97e9dcc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"920816fa0c6b4ad9953154016f525366d5a914d8a602130ee5fa211e97e9dcc8","first_computed_at":"2026-05-18T00:52:12.655103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:12.655103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPOBpRLjE7IdZV8S5ZMyYQ49brPxo7fi8Lhvd796ILoZ4d+qxMvEqfMM0s3ZVcEfLVZDD4/m52nBloEuE+MAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:12.655771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4ce2ca8d833662bbb070e15984dfd7395cf8b9012aec59ffc69e6941debd57e","sha256:511ed5583c9510bdc237d6724f6758b87bec81875195a1ed5fc137ac8e5cf235"],"state_sha256":"7cc819b4e787497d1e139f0d0e5ef5b3f7c9e8c041c9b18c5881b567c14697c6"}