{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LUJXS67E2NAI7R2UPY625JEKLL","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":"46dc3d4b4a1cc2502212d87682a8b10407c205c3772b756b8d937a1c4beb8d02","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-08-20T03:53:20Z","title_canon_sha256":"092b917102a34837626a6eeff12f572b58cdf9b75d5fd2caef6c3d6b0b952154"},"schema_version":"1.0","source":{"id":"2508.14400","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.14400","created_at":"2026-07-16T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"2508.14400v3","created_at":"2026-07-16T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14400","created_at":"2026-07-16T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"LUJXS67E2NAI","created_at":"2026-07-16T01:22:26Z"},{"alias_kind":"pith_short_16","alias_value":"LUJXS67E2NAI7R2U","created_at":"2026-07-16T01:22:26Z"},{"alias_kind":"pith_short_8","alias_value":"LUJXS67E","created_at":"2026-07-16T01:22:26Z"}],"graph_snapshots":[{"event_id":"sha256:11da478559783b926de0423be6410bff74a98630e98e9b8320410e99b4f4df61","target":"graph","created_at":"2026-07-16T01:22:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.14400/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has been studied previously for $k=1$ (i.e., maxima). However, in many applications, a general $k$ ($k\\geq 1$) is of great interest. We provide the upper bounds for the errors between Gaussian approximations and Gaussian multiplier approximations. The dimension $p$ is allowed to be larger than the sample size $n$. The effectiveness of the proposed methods is de","authors_text":"Liuquan Sun, Luobin Zhang, Qizhai Li, Yixi Ding, Yuke Shi","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-08-20T03:53:20Z","title":"Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14400","kind":"arxiv","version":3},"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":"sha256:8a0868497279eb24463a479cf30b220c056242503c5be0b7f15c1806df72fc4f","target":"record","created_at":"2026-07-16T01:22:26Z","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":"46dc3d4b4a1cc2502212d87682a8b10407c205c3772b756b8d937a1c4beb8d02","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-08-20T03:53:20Z","title_canon_sha256":"092b917102a34837626a6eeff12f572b58cdf9b75d5fd2caef6c3d6b0b952154"},"schema_version":"1.0","source":{"id":"2508.14400","kind":"arxiv","version":3}},"canonical_sha256":"5d13797be4d3408fc7547e3daea48a5af6bac776a2051cb567355d7e4861cc75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d13797be4d3408fc7547e3daea48a5af6bac776a2051cb567355d7e4861cc75","first_computed_at":"2026-07-16T01:22:26.864366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:22:26.864366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Px9pEoZB8bUGfI/LUERx5ijtAc+U/8Ks3eBI6di5Wu4/IZ+TZ3M25e3Z37zByfZflxOVfTdxoRLG4FMApIyGCQ==","signature_status":"signed_v1","signed_at":"2026-07-16T01:22:26.865269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.14400","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a0868497279eb24463a479cf30b220c056242503c5be0b7f15c1806df72fc4f","sha256:11da478559783b926de0423be6410bff74a98630e98e9b8320410e99b4f4df61"],"state_sha256":"c80e140f16b8ff7d16040210f21f6fe4c714b1a22e262aba846087a3b8e2f06f"}